Whether to use see or watch is another question regarding stative or active verbs.
See in the stative form (meaning it can’t be progressive) refers to a mental rather than a deliberate activity, such as experiencing the sense of sight (I see the monument every day on my way to work), or declare understanding (Do you see what I mean?).
You can use see in the active form (meaning it can be progressive), when you are referring to a meeting or appointment that is organized at a set time (such as noon tomorrow, or later this evening).
What to do: When you feel like using see in the active form, ask yourself if the action takes place at a set time. If so, go ahead and use any verb tense that fits your meaning. If the action is deliberate, using watch is better.
Look at these examples:
- We’re seeing a movie tonight. (correct)
- We saw a movie last night. (correct)
- We watched a movie last night. (correct)
- While we were watching a movie, we heard a noise from the kitchen. (correct)
- While we were seeing a scary movie, we heard a noise from the kitchen. (incorrect)
One more example might help. Sally is seeing Tommy. This means they have had several meetings with possible romantic intentions. They are dating each other. If you say, “Sally is watching Tommy,” that would be creepy.