conductor vs music director

conductor and music director both are nouns.

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

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

Other synonyms of conductor include director.

conductor (noun)	music director (noun)
a device designed to transmit electricity, heat, etc.	the person who leads a musical group
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