Are Christianity and the Bible the same thing, or are their fundamental differences?
Christianity and Bible are two different things. The Bible is a book, with stories illustrating things that people that came before us thought we ought to know. They often couched it in terms of worship - but for the most part it's "good things to think about." Being kind to your neighbor is a good idea most of the time. This seems like good information. Some of the other information, such as the idea that a man has the right to smack his wife because she's property, or that we should slaughter our neighbors if our offerings to Deity offend them: well, those are clearly not very useful stories, and for the most part I ignore them. They're blatant contradictions of the Useful Information that the book provides. That probably means they're projections by the authors, which honestly pretty much mars it more than a bit. But it's also a pretty big book. And the Bible is one of the books that impacts other literature in Western culture the most.
Christianity, on the other hand, is a group of people's interpretations of the Bible. I don't really want to just lump them into one category, either. Some are interesting to know and enjoyable to be around; others can be obnoxious and insist their Book is 100% true and factual and that anything which contradicts this is a sign of the devil, and evil. Based on their rather limited viewpoint, I choose to avoid these people much as I might, say, avoid men known to brandish guns when drunk.
Which, I think, is a pretty common-sense and grounded answer, right?
Anyway, why is this relevant to magick? I think one little factor illustrates a possible example, and I'll explain why. It revolves around a complaint from Bishops for nearly four hundred years in the middle ages. (Check out "Magic in the Middle Ages" if you want to backcheck this). The problem was this: those goddamn commoners kept stealing the host! The lower class farmers would take the host back to their homes, inscribe runes or talismantic sigils on it, and then bury it in their fields to cause the crops to grow, stick it in the barn so the horses got stronger, near the cows to get them fat. The host was the representation of the living/resurrected body of Christ. This absolutely horrified the Catholic clergy, who realized the Body of Christ was being defiled for personal ends! (Which, by the way, would be a sin.) None the less it illustrates that no matter how hard you stamp down on something, when you claim an idea has power people will try to bend it to their own ends. The human mind was designed to play with things like ideas and try to puzzle out questions. "How do I play with the Universe?" is one of those questions. The person that asks that is the sorcerer/magician/witch/shaman/wtfever. It's what we do. It's what we were made to do, along with asking every other question in the universe. And that makes it and all other questions relevant regardless of what time, age, or quality you live with.