Can you please explain what the difference is between "see" and "watch"
example which is correct?
"Do you want to see a movie?" or "Do you want to watch a movie?"
see = perceive with the eyes, but with an additional meaning of "to watch something"
I can see the cinema over there.
I want to see the film it is showing.
watch = look at something for a period of time.
I watched the programme on TV last night.
Did you watch the film yesterday?
In your two examples, "Do you want to see a movie" implies going to the cinema, whereas "Do you want to watch a movie" implies you will watch it on TV.
In general use, to ask about going to a cinema, you would use "see".