vaudeville theatre vs theater

vaudeville theatre and theater both are nouns.

Word	Noun	Adjective	Verb	Adverb
vaudeville theatre	Yes	No	No	No
theater	Yes	No	No	No

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

vaudeville theatre: a theater in which vaudeville is staged
theater: a building where theatrical performances or motion-picture shows can be presented

Other hypernyms of vaudeville theatre include house, theatre.

vaudeville theatre (noun)	theater (noun)
a theater in which vaudeville is staged	a building where theatrical performances or motion-picture shows can be presented
	the art of writing and producing plays
	a region in which active military operations are in progress