How is Twitter different from Facebook status updates?

Everyone seems to be riding the Twitter train now and I’m thinking of joining the ride. But I don’t entirely get it, so I thought you guys could explain what I’m missing. It’s just a page of status updates, right? Why wouldn’t you just update on Facebook? And how come the Facebook people didn’t think of this and just offer a feed of status updates from there, if that’s what people want?

Hmm. I’m definitely missing something. Please explain.