Ok, This site says "I watched that film" is the same as "I saw that film"
- entertainment and sport Both see and watch are used when you are talking about entertainment or sport.
When you go to the theatre or cinema, you say that you see a play or film.
I saw that movie when I was a child.
We saw him in 'Hamlet'.
Don't say that someone 'looks at' a play or film. Don't say, for example 'I looked at that movie'.
You say that someone watches television. You can say that someone watches or sees a particular programme.
He spends hours watching television.
He watched a rugby match on television.
I saw his speech on the news.
Similarly, you say that someone watches a sport such as football, but you can say that they watch or see a particular match.
More people are watching cricket than ever before.
Did you watch the game last night?
Millions of people saw the World Cup Final.
However, in the dictionary, see in this meaning is not usually used in the progressive tenses
See: [transitive] (not usually used in the progressive tenses) see something to watch a game, television programme, performance, etc.
Did you see that programme on Brazil last night?
In the evening we went to see a movie.
Fifty thousand people saw the match.
So, it is ok to say: I am watching a film
but is it ok to say: "I am seeing a film"?