ballet dancer vs dancer

ballet dancer and dancer both are nouns.

Word	Noun	Adjective	Verb	Adverb
ballet dancer	Yes	No	No	No
dancer	Yes	No	No	No

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

Other hypernyms of ballet dancer include professional dancer, terpsichorean.

ballet dancer (noun)	dancer (noun)
a trained dancer who is a member of a ballet company	a performer who dances professionally
	a person who participates in a social gathering arranged for dancing (as a ball)