dancing-master vs dancer

dancing-master and dancer both are nouns.

Word	Noun	Adjective	Verb	Adverb
dancing-master	Yes	No	No	No
dancer	Yes	No	No	No

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

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

dancing-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)