Movies is slang for a motion picture. Film is the medium on which motion pictures are fixed. Cinema is from the French cinématographe which comes in part from the greek kinema, meaning movement. So cinema is really just another word meaning moving picture. It also has come to mean more generally the process of film-making and also the building where films are shown. Theater is similar to cinema, in that it can mean the building, or more generally the industry of live performance (i.e. plays, musicals, etc).
Film, movies, and pictures are used interchangeably:
I saw a film. I saw a movie. I saw a
In context, the theater is the building where movies are shown, but usually people would specify the movie theater to avoid confusion with the live theater.
"Movies" and it's short-lived companion "talkies" describe in a very simplistic way, what it going on on the screen. Things are moving: movies. People are talking: talkies.
Movies and pictures can be used interchangeably:
I'm going to the movies/pictures.
But pictures is mainly a UK expression.