theater vs cinema

theater and cinema both are nouns.

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

As nouns, cinema is a hyponym of theater; that is, cinema is a word with a more specific, narrower meaning than theater:

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

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