theatre director vs theater director

theatre director and theater director both are nouns.

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

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

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

Other synonyms of theatre director include director.

theatre director (noun)	theater 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