music director vs conductor

music director and conductor both are nouns.

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

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

Other synonyms of music director include director.

music director (noun)	conductor (noun)
the person who leads a musical group	a device designed to transmit electricity, heat, etc.
	the person who leads a musical group
	the person who collects fares on a public conveyance
	a substance that readily conducts e.g. electricity and heat