dancing-master vs teacher

dancing-master and teacher both are nouns.

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

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

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

dancing-master (noun)	teacher (noun)
a professional teacher of dancing	a personified abstraction that teaches
	a person whose occupation is teaching