Satan, A.K.A. Lucifer the fallen angel, is part of the Christian pantheon. If you believe in God, by extension you have to believe in Satan.
Atheists, Muslims, Buddhists, etc. don't recognize the existence of Satan. (Islam does have a similar figure to satan, but he's not a fallen angel and isn't referred to as Satan.)
To sum up, Satanism and Satan Worship are offshoots of Christianity. Satan Worship is just what it sounds like. Satanism, I'm told is not the worship of Satan but an attempt to follow his path and his choice,"I will not serve." I think it's more about doing what you want regardless of what anyone else says or does. (In other words, justification for being a self centered ***hole)
Fred
P.S. Boy, we've gone off topic here!