That sounds fine in theory but such distinctions are often subtle to say the least.
For example, for many centuries after the rise of the Christian religion in Europe, even though there were other, even older sects of Christianity (such as the Copts and the Eastern Orthodox), Roman Catholicism was widely acknowledged by those who had influence to be THE CHURCH, encapsulating Christianity.
It took more than a millenium before any serious challenge to that concept came forward, with the Reformation, and still even today you have a tacit acknowledgement by folks like the Archbishop of Canterbury, that the See of Roman is preeminent.
During that period, "the Church (meaning the Roman Church)" and "Christendom" were considered synonymous in the minds of those people who lived and wrote with great influence on generations that came after them. Thus, it was very, very hard to distinguish between "religion" and "church" except to a comparative few.
OTOH, you have Islam which it seems to me has always been highly decentralized, venerating "places" only symbolically (Mecca the CITY, not the SEAT of Islam, is what they bow down to pray toward). It is interesting to read some of the websites that Muslims themselves have set up to discuss their religion. They seem to have only in the last few centuries, "fractured" enough to begin to argue in the same sectarian way the Christians have been doing for five hundred years (or longer if you count some of the "heresies" such as the Albeghensians (sp) that only just missed becoming bona fide SECTS due to their reliance on charismatic leaders who were swiftly killed by the Establishment).
And one of the BIGGEST arguments, at least according to my own inquiries into the matter, seem to turn on the question of "what is PURE Islam?"
Sound familiar?
Thought this might interest you.
It took more than a millenium before any serious challenge to that concept came forward, with the Reformation..." More churches. This is why some of our friends say, "I atten a Lutheran Church."
A church is a social institution that promulgates a particular religious doctrine. Similarly, --- and please do not read any kind of insult here, none intended --- a coroporation is a social institution that produced a good or a service. A family is social institution, endemic not to humans only, for procreation of species.
This is different from the religion iteslf, which is a system of values, rules, notions, etc. The distinction here is similar to that of "mathematics" and "Mathematics Department" at a university. The former is a body of knowledge, and the latter, of course, is a social insitution for the promulgation thereof.
Now, And one of the BIGGEST arguments, at least according to my own inquiries into the matter, seem to turn on the question of "what is PURE Islam?"
is a theological question. That is, it concerns with religion. Suppose there are three answers: A, B, and C. Those who follow these interpretations will form "A Church," "B Church," and "C Church," respectively. Each of them will believe that their is PURE Islam. This is what seems to have happened in Christianity, Judaism, and Muhammedism.