little theater vs theatre

little theater and theatre both are nouns.

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

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

little theater: a small theater for experimental drama or collegiate or community groups
theatre: a building where theatrical performances or motion-picture shows can be presented

Other hypernyms of little theater include house, theater.

little theater (noun)	theatre (noun)
a small theater for experimental drama or collegiate or community groups	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