This page has three major sections. The first two review the Catholic and then the Protestant perspectives on the Church. The third section deals with the question of why there are so many churches.
The term "Church" is used by Christians in two different, but closely related, ways. It can refer to all of Jesus' followers, viewed as a community. It can also refer to specific institutions, either the local congregation or a national or international body. It can even be used to refer to the building in which they meet.

The Church is important, because God does not save people in isolation. An important part of what needs to be restored is our relationship with other people. That can only be done by the community as a whole.
God most often reaches us through other people. Mother Theresa's statements about seeing God in the poor are just one example of a more general Christian principle. Because a large part of our problem is self-centeredness, a large part of the remedy is to learn to depend upon other people, to represent Christ to them and allow Christ to speak to us through them.
The Church is also the group with which we worship. As such it has the responsibility to preach the Word of God, and to administrator the sacraments. (See the section on worship for a discussion of the sacraments.) These are critical elements in maintaining our fellowship with God and each other.

The Church also has a responsibility to encourage its members to make spiritual progress, and to show their faith by their behavior, both through their ethics and their good works. This responsibility includes administering brotherly correction when someone errs. Traditionally the Church has felt a responsibility to discipline, and if necessary exclude, members whose public lives are not in keeping with the message of Christianity. Not all churches are equally careful about carrying this out. It is in fact one of the more difficult responsibilities to get right. It is very, very easy for Church discipline to lead to self-righteousness and intolerance.

Jesus referred to the Christian community with several metaphors. In one he said that he was the vine, and all of his followers are the branches. In another, he referred to the church as his body. All of these images emphasized that his followers are spiritually united with him and with each other. One of the major problems today is that this union is not completely reflected in the way Christians act.

In this page, I will normally be using the term "Church" to refer to the universal Church. However I will sometimes use it to refer to individual communions such as the Catholic Church.

I. THE CATHOLIC PERSPECTIVE
The Catholic and Orthodox traditions see the church as the successor to the "Apostles" (Jesus' original followers). Jesus gave the apostles authority to lead the community and make decisions for them. He also gave an assurance that the community would be guided by the Holy Spirit, and would be protected.

Organization
By the end of the 1st Century, authority in the Church centered on bishops. Bishops were seen as successors to the Apostles. Bishops are consecrated by other bishops (normally at least three). So in principle every bishop can trace their authority back through an unbroken line of consecrations to the Apostles, and then Christ. This is referred to as the "Apostolic succession".
Currently bishops are normally responsible for a city and the surrounding territory. Of course the exact area depends upon population density and other considerations.

Bishops have several different kinds of authority and responsibility. They have the responsibility for maintaining proper doctrine in the area for which they are responsible. They are responsible for the proper conduct of the sacraments. They normally conduct certain sacraments (e.g. confirmation) personally. In other cases they delegate the authority to priests.
During the first few centuries, certain bishops developed greater prestige than others. This was often because of the history or role of their cities. The bishops of these key cities have special leadership responsibilities. In the East, they are referred to as "patriarchs". In the West, the bishop of Rome is regarded as the preeminent bishop. He is normally referred to as the "Pope". (Note that "pope" is another word for patriarch. In principle any patriarch can be referred to as a pope. However currently this would be so confusing that the term pope is normally reserved for the bishop of Rome.)
The Pope has two conceptually separate roles: First, he is the patriarch of the Roman Catholic Church. As such, he is ultimately responsible for everything that happens in that communion. He makes key appointments and decisions, and can review any action.

In the Catholic tradition, the Pope is also seen as the spokesman for the Church as a whole. He has a special responsibility for maintaining proper doctrine and morals. As part of this responsibility, he or his representative chairs all ecumenical councils. He may also make authoritative doctrinal decisions on his own authority. Of course this authority comes from Christ. See the discussion below of Papal infallibility.

In principle the second role gives him leadership responsibilities over churches other than the Roman Catholic Church, i.e. churches of which he is not the patriarch. In such churches the Pope would not directly govern, but they would still be subject to his overall doctrinal leadership. There are a few Eastern churches that accept this concept. (They are often referred to as "uniat" churches.) However the major Orthodox churches do not accept the Pope's idea of universal leadership. Many of them would accept him in some role of spokesman. But generally they do not accept papal infallibility, and they also believe that he has often attempted to make decisions for other churches that are properly the responsibility of their own leadership.

The Catholic and Orthodox traditions emphasize continuity in doctrine and in worship. Please see the latter parts of Why do Christians Believe This? for the role of tradition in developing and stabilizing doctrine. The bishops have a primary role as carriers of the tradition. They are expected to hold to the original faith as given to the Apostles, and also to work together and with the Pope (or all the patriarchs, for the Orthodox) to maintain common doctrine and practice throughout the Church.
The office of priest developed slightly later. Originally they were seen primarily as assistants to the bishop. Priests are typically responsible for an individual congregation or church. This isn't exact: Larger churches may have more than one, and sometimes a single priest may have more than one church. The priest is responsible for guiding the life of the congregation, and for conducting most normal sacraments. Priests are ordained by bishops.

Certain of the sacraments (e.g. communion) may only be performed by a priest or bishop. This is not just an issue of who has permission to do it. At ordination, a priest receives spiritual authority. Without that authority, the transformation of the bread and wine into Christ's body and blood in communion will not occur.

Authority
Two distinguishing characteristics of the Catholic Church are its concept of teaching authority, and its approach to church

discipline.
Catholics believe that the Church was given authority by Christ to make decisions. These include both doctrinal and moral issues. This authority is lodged primarily in the bishops and the Pope. In appropriate circumstances, their decisions can be infallible. The teaching authority of the Church is referred to as the "magisterium". Catholic writers sometimes distinguish between the "ordinary magisterium" and infallible teaching.

The ordinary magisterium is the teaching responsibility as carried out through ordinary preaching and catechesis, as well as through specific pronouncements such as encyclicals and pastoral letters. Although teachings of the ordinary magisterium are not exactly infallible, they are part of a process that is guided by the Holy Spirit. Thus it is expected that Catholics will receive such teaching as authoritative.

Catholics also believe that is possible for the Church to make infallible decisions. There are two ways of doing this: an ecumenical council, and a direct papal decision. When an ecumenical council makes doctrinal decisions, in union with the pope, they may be infallible. In addition to this, the pope himself may make infallible decisions.

The concept of papal infallibility is often misunderstood. It does not mean that everything the Pope does is perfect. Many popes have been seriously flawed. Rather, the belief is that the Holy Spirit guides the Church in such a way that when the Pope makes certain solemn pronouncements in the areas of faith and morals, those pronouncements are infallible. The Pope has this role because he is the one who speaks for the Church as a whole.

This class of pronouncement is referred to as "ex cathedra" ("from the chair", i.e. the official bishop's throne). All Catholic scholars agree that there have been two infallible pronouncements. Many have longer lists, up to about 20 items. (Note that there is not an infallible list of infallible pronouncements.) These are in addition to documents produced by church councils. They may also be regarded as infallible. But they are not specifically based on exercise of papal infallibility.

Historically, Catholics have been very concerned about maintaining high moral standards among their members. Members are required to confess their sins to a priest. The priest is expected to provide both spiritual and ethical guidance.
The Catholic church has a set of rules describing the way it functions. These rules also cover a variety of moral issues, as well as procedures for marriage and other church activities. This is referred to as "canon law". The most complex and problematical parts tend to focus on sexual matters, particularly on the regulation of marriage and annulment.

Marks of the Church
For the Catholic tradition the key marks of the Church are defined by four phrases used in the Apostles' creed: It is the one, holy, Catholic, and Apostolic church.

The term "Catholic" means "universal". The Church is universal, and it is one. Its doctrines can be traced to the Apostles.
Of course there is some question how literally the Church can be said to be one at the moment. There are at least three major branches of the Church. However both the Catholic and Orthodox traditions believe that they maintain the full continuity with the original Apostles, and thus that in some sense the entire body of Christ is centered in their community. Other Christians participate in this unity in an incomplete sense.

II. THE PROTESTANT PERSPECTIVE
For Protestants, these issues are more complex, because there are more Protestant churches. See below for the question "Why are there so many Churches?".
Protestants tend to distinguish between the Church as the universal body of Christ and individual organizations. To avoid confusion, the individual organizations are often referred to as "denominations". Protestants also accept the Apostles' creed, so they agree that the Church is one and universal. However they tend to see its unity and universality as being a spiritual matter. It is a consequence of our unity in Christ. It need not be reflected in a single organization.

Organization
In general Protestants vary a lot in the way that their churches are organized. There is far more variation here then in beliefs and practices. Many Protestants would say that a single scheme of church organization is not described in the Bible, although certain guiding principles are given. This leaves individual churches free to adopt different patterns.
Protestant churches may be classified on a spectrum with "connectional" churches on one end and "congregational" churches on the other end. In connectional churches, there are national and regional bodies, which have a good deal of authority. Quite often higher-level bodies review what lower bodies do, and can take action to overrule them. In the Presbyterian Church, it is possible for a Presbytery to unseat the Session (governing board) of a local church, and appoint its own governing board. This is typically done in a situation where there is a conflict within the local church that it does not appear the church can handle for itself. In some connectional churches (e.g. the Methodists), pastors are assigned to local churches by a central authority (in this case the bishop).

In congregational churches, each congregation is independent. They call their own pastor and make their own decisions. No higher level body can intervene. Many congregational churches still have national and regional organizations. They coordinate programs that require cooperation beyond a single congregation, e.g. sending missionaries, preparing Sunday School curriculum material, and running seminaries (colleges for training pastors). However a few traditions (particularly more conservative portions of the Church of Christ) do not believe that any higher level body is permissible, even for voluntary cooperation.

There is quite a variety of patterns between these two extremes.
Protestant Churches base their organization on a few common patterns. Many Protestant churches have bishops. Except in a few cases (Anglicans, Lutherans in Scandanavia), these bishops do not have the Apostolic succession. They are simply elected by the church as leaders. Thus these bishops are sometimes called "titular bishops", to distinguish them from canonical bishops that do have the Apostolic succession. In general the Lutheran and Methodist traditions include bishops. Since the Pentecostal and Holiness churches are developments from the Methodists, they often have bishops as well.
Almost all Protestant churches have elected leaders. Normally there is a governing board of some sort for the local church. For connectional denominations, the national and regional levels also have elected groups that function more or less as legislatures. (The U.S. government is modeled after Presbyterian church government.) Clergy and bishops (if any) normally serve in these bodies, either as part of a single body or (in a few churches) as a separate "house", like the Senate and House of Representatives.

Protestant Churches try to base their church organization on the Bible. While the Bible doesn't give a specific plan of government, several offices are referred to. These include deacon, elder, bishop, and apostle. Not all churches use all offices. Most churches believe that the office of apostle applied only to Christ's followers, and that there are no longer apostles. Some identify two offices, or split a single office into two variants.

In the Catholic and Orthodox traditions, there is a clear distinction between "lay people" and "clergy": clergy have been ordained. Ordination is a sacrament, which imparts a permanent metaphysical mark on the soul. Clergy include bishops and priests, and in some sense also permanent deacons.

For Protestants, this sort of distinction is not as clear. Protestants do have leaders that more or less correspond to priests. They are commonly called pastors or ministers, though a few Protestant groups use the term "priest". Pastors commonly have special education, either a graduate degree or training at a Bible college. They are commonly full-time. They are normally ordained. That means that they are set apart in a special ceremony, and that they have the authority to celebrate baptism and communion.
However for Protestants, ordination doesn't confer any special metaphysical powers. The fact that only pastors lead in a communion service is a matter of church order. It is not -- as in the Catholic tradition -- that only they have the power to make bread and wine change into Christ's body and blood.

Protestants often use the term "lay" to refer to everyone other than pastors, although it's not clear to me that the lay/clergy distinction is actually consistent with Protestant theory. In all Protestant churches that I know, each congregation has lay leaders that serve alongside the pastors. Their exact relationship varies by denomination. However the lay leadership tends to have a stronger role for Protestant churches than for Catholic ones.

The exact set of lay leaders varies. However one common pattern has deacons and elders. In this pattern the deacons are typically responsible for charitable activities, and elders for policy decisions. However not all churches use both deacons and elders.

In the Reformed tradition (which includes Presbyterians), all leaders are ordained. Since the distinction between lay and clergy was traditionally ordination, in some sense this means that Reformed churches have no lay leadership. However for most purposes Reformed deacons and elders are thought of as lay: they are not full-time positions. The positions tend to rotate among the active members of the congregation.

Authority
Protestants do not believe that the Church is infallible. Indeed they believe that it has made errors. They do accept that the Holy Spirit guides it. However since the Church is made up of human beings, it may take wrong turns and have to be corrected or renewed.

Since they believe that organizations and leaders may go astray, organizational continuity is not as important. Protestants are primarily concerned with whether a group's views and practices are consistent with the Bible, and to a lesser extent with the early Church. This has more importance than whether a group can show that its leaders trace their pedigrees back through a continuous set of bishops to the Apostles.

Protestants do not place as much emphasis on either the Church as an organization or on the authority of its leaders. They see the Christian community as important. But they are not convinced that the sort of authority Catholics and Orthodox lodge in the leadership has justification in the Bible, nor that it has worked out well. Indeed Protestants tend to see the Catholic hierarchy and canon law as being very similar to the Jewish leaders and legal tradition which Jesus opposed.

Protestants do not normally confess their sins directly to a pastor. This means that they do not have the same kind of detailed supervision of their lives that Catholics do. This is one reason that there is no need for canon law: the moral components of canon law evolved to guide priests as they supervised their members' lives.

There are clearly advantages and disadvantages to each approach. At its worst, the Catholic approach can turn into barren legalism. Personal reports from Catholic friends suggest that it may also lead to dishonesty. (I'm told that it is very naive for me to assume that all Catholics confess to the priest honestly.) However Protestant practice runs the risk of encouraging members to be morally lax. The detailed supervision provided by regular confession is one of the primary methods of accountability. To replace this, many Protestant groups encourage members to meet together in small groups or as partners. In these groups they are expected to share enough about their lives that they can hold each other accountable before God.

Marks of the Church
Protestants also accept the characterization of the Church as one, holy, catholic, and Apostolic. However when Protestants say they believe in the holy catholic Church, they are using the term "catholic" in its original meaning of "universal". That is, they are pointing to the fact that all Christians are united because of our common relationship with Christ. Protestants do not identify the unity of the Church with a single organization such as the Catholic Church. Indeed they find that whole approach odd, given that there are now at least two major groups claiming to be identical with the universal church: the Catholics and the Orthodox. (Some other groups make this claim as well, such as the Mormons and Jehovah's Witnesses.)

Protestants traditionally have identified two or three key marks of a true church. Most Protestant writers believe that in order to have a true church, the Gospel must be properly proclaimed, and the sacraments properly administered. By proper, it is normally meant that all the essential Scriptural aspects of the Gospel are preached, and that it is not adulterated by other things. Similarly, the sacraments are administered as they are defined in the Bible, and they are not combined with superstitions or other improper additions. Some writers identify church discipline as a third essential mark of a true church. However others regard it as important but not essential. That is, they would not reject a church as being a true church because it has not managing to maintain discipline among all its members.

III. WHY ARE THERE SO MANY CHURCHES?
Because people are imperfect. The ideal that Jesus taught was very clear: All of his followers were to form a single community, united in him. He used the image of a vine and its branches.
Unfortunately Christians have often been unable to agree on matters of belief and practice. In many cases the disagreements have been serious enough that it would be difficult for both approaches to coexist. Thus it has often been necessary for the groups to separate.

Multiple Churches Do Not Always Reflect Serious Disagreements
The differences are often exaggerated. The first thing to note is that not all churches were founded because of disagreement. Many Christians consider the basic unit of Christian action to be the individual congregation. Larger bodies, such as national churches, exist as a matter of convenience, to help congregations do things that require cooperation. Thus many Protestants do not particularly want a single, huge organization that includes all Christians. For those who take this approach, the unity of that Jesus was talking about is a spiritual one, not a bureaucratic one.

The second thing to note is that disagreements among Christians are usually over details of how we go about implementing Jesus' teachings. There is agreement about many beliefs and practice. Thus books such as C. S. Lewis' "Mere Christianity", or Kreeft and Tacelli's "Handbook of Christian Apologetics" can contain fairly substantial presentations of Christian beliefs that would be acceptable to just about all Christians.

In my opinion the most significant differences within Christianity fall into three categories: marginal groups; the long-standing differences among Protestant, Catholic and Orthodox; and the reaction to liberalism.

Marginal Groups
This document tries to present a "generic" Christian viewpoint, which would be acceptable to most Christians. However there are a few groups whose ideas are far enough away from the mainstream that it is nearly impossible to include them and still say anything of substance. In general I classify a group as "marginal" when it rejects major doctrines such as the Trinity or Incarnation. As far as I know, all groups that do this also differ from the mainstream in significant issues of practice as well.
The best-known groups of this sort are the Jehovah's Witnesses and the Mormons. Both of them differ significantly with the mainstream on the nature of God and Jesus. The Mormons are large enough (and are growing fast enough) to be a significant force. There are a number of smaller groups with similar properties. A number of people who reject the Trinity are active on the Internet. This tends to make it appear that there is more opposition to common doctrines such as the Trinity than actually exists.
The Major Groupings: Catholic, Protestant, Orthodox

The second major division in Christianity involves the three major groupings: Catholic, Protestant and Orthodox. As the Roman empire disintegrated, the Church divided into Eastern and Western portions. In my opinion, this was a consequence of the difficulty in communication and transportation. There simply wasn't good enough coordination to deal with differences as they began to develop. Although there were few major differences in theology, there were differences in emphasis. The East also objected to the growing power of the Pope. As a result, Eastern and Western Christianity split into what is now referred as Orthodox (Eastern) and Catholic (Western) branches. These groups are still separate, although generally they acknowledge the validity of each other's sacraments, and agree on most of the key doctrines.

In the 16th Century, the Western church split further into Catholic and Protestant streams. Protestants believed that the church had slowly drifted from Jesus' intentions. Major issues involved the nature and authority of the hierarchy, the differences in role between clergy and ordinary Christians, and what Protestants saw as superstitious or unjustified practices in worship. The Anglicans could be regarded as a separate stream. They combine some of the emphases of Catholic and Protestant thought, and sometimes try to mediate between them.

The Protestant branch has further fragmented, with a dozen or so significant schools of thought, and innumerable individual churches. The peak of this fragmentation seems to have been in the 19th Century. Most of the current schools of thought appeared then, and there have been few major new ones in the 20th Cent. In the 20th Century, a few of the larger groups have reunited. There is also a growing degree of cooperation among the different groups. As mentioned above, many Protestants do not regard it as important to create a single organization. They see that as likely to create a hierarchy that is out of touch with the needs of the people, and as requiring compromises that would result in a watered-down, "lowest-common denominator" theology. Thus most Protestants now see Christian unity as being founded in a common relationship in Christ, and expressed in mutual respect and cooperative activity, but not in a single organization.

For Catholics and Orthodox, this situation is a serious problem. They see the Church as an organic whole, with an organizational unity that reflects our spiritual union in Christ.
This excerpt from the website http://geneva.rutgers.edu/src/christianity/index.html