dance master vs dancer

dance master and dancer both are nouns.

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

As nouns, dancer is a hypernym of dance master; that is, dancer is a word with a broader meaning than dance master:

Other hypernyms of dance master include professional dancer, terpsichorean, instructor, teacher.

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