director vs film producer

director and film producer both are nouns.

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

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

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

director (noun)	film producer (noun)
someone who controls resources and expenditures	a producer of motion pictures
the person who leads a musical group
someone who supervises the actors and directs the action in the production of a show
member of a board of directors
the person who directs the making of a film