As far as I know in America they do say to see a movie.

I think it's better to use the verb WATCH instead SEE.'Cause in English they say:watching a movie but I never heard seeing a movie.

"<em>Is there any native wanna give us the reason why sometimes you use 'see' and sometimes use 'watch'</em><em>?</em>"

I've never really thought about this before, but as a general rule of thumb, you use the verb "to see" if you actually go to the cinema. 

E.g.

Person 1: Does anyone fancy going to the cinema?

Person 2: Yeah, what do you want to see?

Person 1: Do you want to go see Batman tonight?

Person 2: Nah, I think I'll sit in and watch something on Netflix.

Is there any native wanna give us the reason why sometimes you use 'see' and sometimes use 'watch'?

I watched Temptation : Confession of a Marriage Counselor.

I watched The Two Towers yesterday, I love The Lord of the Ring.