film director vs film producer

film director and film producer both are nouns.

Word	Noun	Adjective	Verb	Adverb
film director	Yes	No	No	No
film producer	Yes	No	No	No

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

Other hypernyms of film director include film maker, filmmaker, movie maker.

film director (noun)	film producer (noun)
the person who directs the making of a film	a producer of motion pictures