An interesting question. In many cases, there is no difference at all. If you ban a book, you censor it. In fact, if you look at the website listed below, you'll see that the writers use the terms interchangeably.
Now, if you want to be picky, banning is an either/or decision: either something is banned or it is not. However, you can censor something without banning it. You can, as sometimes happens on television, "bleep" out the obscenities, for example, or cover up the offending portion of work of visual art.