theater director vs supervisor

theater director and supervisor both are nouns.

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

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

theater director: someone who supervises the actors and directs the action in the production of a show
supervisor: one who supervises or has charge and direction of

theater director (noun)	supervisor (noun)
someone who supervises the actors and directs the action in the production of a show	a program that controls the execution of other programs
	one who supervises or has charge and direction of