dancer vs dance master

dancer and dance master both are nouns.

Word	Noun	Adjective	Verb	Adverb
dancer	Yes	No	No	No
dance master	Yes	No	No	No

As nouns, dance master is a hyponym of dancer; that is, dance master is a word with a more specific, narrower meaning than dancer:

dancer (noun)	dance master (noun)
a performer who dances professionally	a professional teacher of dancing
a person who participates in a social gathering arranged for dancing (as a ball)