"cinema" and "movies" are interchangable for the place you to go watch a film - I am going to the cinema/movies. film and movie are the thing you watch. We are going to watch a film/movie movies is also the plural of movie

film = in British accent movie = in American accent movies = movie plural cinema = the place that you are going to watch movies in . ex: Would you like to go to the cinema with me , they will play some new movies this week ?

I'm going to see a film I'm going to see a movie. I'm going to the cinema. I'm going to the movies. That is how it's done!