home theater vs home theatre

home theater and home theatre both are nouns.

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

As nouns, home theater and home theatre are synonyms defined as:

home theater and home theatre: television and video equipment designed to reproduce in the home the experience of being in a movie theater

home theater (noun)	home theatre (noun)
television and video equipment designed to reproduce in the home the experience of being in a movie theater	television and video equipment designed to reproduce in the home the experience of being in a movie theater