Twitter is designed as a mini-blog: you get 140 characters to tell people what you're up to, send them to interesting stuff on the web, etc.
I think of Facebook as more of a combination online bio/chatroom. Instead of just chatting, you can also make a page about yourself with lots of information.
Also: Facebook has cute gimmicks, like 'presents' you can send your friends and other fun/irritating applications, like quizes. If you are having a party, you can make a special page devoted to the event, then invite your friends, manage the guest list and so on.
Facebook has a lot more functions than twitter, which is leaner and more nimble.