Last year's thread called Is self-injury considered an addiction? may be helpful for differentiating between the two, especially the post by HeartArt that gives excerpts from other sources like GoAskAlice.
Maybe one of the differences between an addiction and a compulsion is that with an addiction, there are usually symptoms of withdrawal when one is deprived of the thing that one is addicted to. I don't know if that's true of a compulsion.
I spend a lot of time on the Internet, and at times become "compelled" to send more e-mails than usual, post on more message boards (like right now, in fact) and so forth. But when I leave my computer, I experience no withdrawal, no overwhelming urge to return to it.