cinema vs theater

cinema and theater both are nouns.

Word	Noun	Adjective	Verb	Adverb
cinema	Yes	No	No	No
theater	Yes	No	No	No

As nouns, theater is a hypernym of cinema; that is, theater is a word with a broader meaning than cinema:

cinema: a theater where films are shown
theater: a building where theatrical performances or motion-picture shows can be presented

Other hypernyms of cinema include house, theatre.

cinema (noun)	theater (noun)
a theater where films are shown	a building where theatrical performances or motion-picture shows can be presented
a medium that disseminates moving pictures	the art of writing and producing plays
	a region in which active military operations are in progress