1. I want to see the movie.
2. I want to see the film.
3. I want to see the motion picture.
4. I want to see the animated picture.
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Ae they all the same in meaning? What is the difference among them?
Almost.
#4 is referring to animation in which the characters and setting are all hand-drawn, not film of real people.
http://en.wikipedia.org/wiki/Animation
#s 2 and 3 refer to movies made with humans and other living beings in them as the actors and (for the most part) settings in which humans move around.
#1 could refer to either one, animation or with humans as the actors. There have been combinations (animation and humans), but those are fairly rare.
Others here may have additional comments for you.