director vs music director

director and music director both are nouns.

Word	Noun	Adjective	Verb	Adverb
director	Yes	No	No	No
music director	Yes	No	No	No

As nouns, director and music director are synonyms defined as:

Other synonyms of director include conductor.

director (noun)	music director (noun)
someone who controls resources and expenditures	the person who leads a musical group
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