theater director vs theatre director

theater director and theatre director both are nouns.

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

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

theater director and theatre director: someone who supervises the actors and directs the action in the production of a show

Other synonyms of theater director include director.

theater director (noun)	theatre director (noun)
someone who supervises the actors and directs the action in the production of a show	someone who supervises the actors and directs the action in the production of a show