They are both correct, though the meaning is slightly different. "Watch" indicates using more attention or focus than "see". In terms of usage, I would say that if you're proposing going to a movie, or talking about it after the fact, it's more common to use "see". For example- "Let's go see a movie!" "Have you seen that movie?" However, it is also OK to use "watch". If there's a movie on and someone asks you what you're doing, you must say "I'm watching a movie". It is wrong to say "I'm seeing a movie" because "see" is a discrete action/event, whereas "watch" is continuing/ongoing.

[American English] In my opinion, when you go "see a movie," you go to a movie theater to see it. You can also see a play, see an exhibition. Watching a movie usually happens at home, or maybe somewhere outside a movie theater. Compare: 1. "I would like to watch a movie tonight. What do you want to watch?" <-- This probably means you're doing it at home 2. "I would like to see a movie tonight." <--This is a little ambiguous, but it most likely means you are going to a movie theater. 3. "I want to go see a movie tonight." <-- This is 100% clear. You want to go to a movie theater to watch a movie.

hi;monti,,yes,,they are both correct,,but they have a different meaning,,like the word "see" see meant your only want to look on it,,but the word "watch" it means you want it complete,,hope you get it.!

Hello Monti, Eli's answer is very good , I will just give some more examples. watch a movie: means to look and observe it attentively while maintaining interest in the activity. " Let me watch this movie, I think it is a very good one". see a movie: to perceive it with the eyes, regardless from the degree of interest or attention. "I don't remember, but I think I have seen this movie".