film director vs movie maker

film director and movie maker both are nouns.

Word	Noun	Adjective	Verb	Adverb
film director	Yes	No	No	No
movie maker	Yes	No	No	No

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

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

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