Do you "watch" a movie or "see" a movie?
Generally, 'see' has the connotation of having gone to the movie theater and watched the movie there whereas 'watch' tends to mean to watch it in a home environment on DVD or TV.
In the cases where 'watch' is used to mean doing so at a theater, it is often accompanied with a construction like "go and", e.g. "We're going to go and watch X." In the absence of other context, this implies the sentence, "We're going to go to the theater and watch X" as opposed to "We're going to go to Bill's house and watch X."
This is just my experience of course.
Also, the distinction doesn't seem to apply to past tense. I mostly hear 'seen' used in this context but sometimes hear "watch"
- Have you seen X?
- Did you watch X?
The first one is much more common in my experience.
Either way, the primary distinction between watching a movie in a home environment and watching it at a theater is probably constructions involving the use of the verb "go".
To "go see something" applies to more than just movies. One can go see a play, an art exhibition, or what's happening somewhere. It's the act of going out somewhere and looking at something. Saying "Let's go see a movie" means that that you will go to the movie theater and watch a movie. When you are actually sitting in the movie theater, you are watching the movie.