See or Watch (a film / a movie)?

You WATCH a movie on TV or DVD etc. or when you are in the cinema, then yes, you ARE watching it.

However, you go to the cinema to SEE a movie, or to SEE a play you go to the theater. After you watch them then you have SEEN them. 

Generally, you go "see" a play or a movie. Once you're there, you may not watch it. You could be too busy necking with your boyfriend, for example.