There are only two basic forms of religion:
Theism and A-Theism
The "third alternative," namely agnosticism, is merely a decision not to vote. This is particularly uninteresting and therefore may be left out of intelligent conversation. If you are an agnostic, I sympathize and hope you find your truth soon. Check under your bed, that's normally where I lose things.
A-theism is a challenging perspective, because in declaring the absence of a higher power one is automatically implying that you are, in fact, the highest authority. What great arrogance that takes! Unless, of course, you are correct. In which case it is lonely perspective, is it not? And, if you are the highest authority, can there ever be one higher? Or are you the pinacle of all you can ever see? As I said, challenging. But, in its own way, powerful.
Theism covers all other beliefs.
Here are the common variations on theism as you wil meet them in the western world:
Deism is a subset of theism where believers accept a benevolent, omnipotent and omnicient God, but not a conscious or personal God.
Judaism is a subset believing in a benevolent, conscious and omnicient God, but not necesarily omnipotent. He created everything, but in the last few millenia things have been getting a little out of hand.
Muslims believe in the same God as above, except that they are the chosen people instead of their half-brothers the jews. No significant theological differences here.
Hindus believe in a series of little God (kind of like angels) created by a conscious omnipotent, omnicient God. He has a SubGod, or angel, who is benevolent, personal and helps out people. Balanced by his brother the god of death. It is these sub-gods that separates Hindus from deists.
Christians believe in a benevolent, personal, conscious, omnipotent, omnicient God. This God has no limitations, nor makes mistakes. He is also three-in-one, the closest to truly polytheistic of all religions. Many branches of christianity believe in salvation through grace.
Mormons believe in a benevolent, personal, conscious, omnicient God. However, he is not omnipotent since he either a)gave that up to create us, or b)is only a God because he was mormon on another planet somewhere, and he didn't really create the universe after all. Like vishnu et al of the Hindu system, we have a hierachy from God the source of all, to Jesus and Satan, the life-bringer and death-bringer respectively.
Scientologists Worship a science-fiction author.
Logicians believe in a omnipotent God. He has no characteristics other than complete constancy and reliability. His name is more accurately Reason, not Logic, and appeals to Him are as iron-clad as they are silly. Many people do not see this as a religion, citing its basis on faith in an unseen power as proof. Cause-and-effect, statistics, and gravity being amung its most famous beliefs. Most so-called atheists fall into this category.
Buddhism is of course, not a religion but a methodology. The underlying belief system is entirely flwexible, although originally Hindu.
Science was meant to be a methodology also, but has become so mired in its own appeals to higher authority that it quickly forces a follower into religion (see logician).
The purpose of both religion and science are to explain the surrounding world, the only difference being the youth of science allows it a closer connection to reality. (Assuming reality exists at all).