Seeing is passive. Watching is active. Seeing something doesn't require any intention on your part, but watching something does. It's the same with hearing and listening.
One can look at it this way; Seeing a movie means viewing with no interest or expectations. On the other hand, watching a movie means you're interested, analyzing it and taking it all in.
I've always wondered about that too, lol. I guess if you "see" a movie, you only glance at it long enough to see it. And if you "watch" a movie, you're viewing the whole thing. :P