They're very similar. You design UI to provide a good UX. A good UX is so because of good UI.<p>The only difference I can think of is that UI may include looking beautiful (gradients, shine), while UX isn't concerned with that. Really, you're talking about similar things.
I've always looked at it as UI is a part of UX. The user interface is just that -- the interface to your site/application. The user interface incorporates the UI, but also includes how it feels to move throughout the UI and traverse and use the site/app.