drum major vs music director

drum major and music director both are nouns.

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

As nouns, music director is a hypernym of drum major; that is, music director is a word with a broader meaning than drum major:

Other hypernyms of drum major include conductor, director.

drum major (noun)	music director (noun)
the leader of a marching band or drum corps	the person who leads a musical group