dancer vs ballet dancer

dancer and ballet dancer both are nouns.

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

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

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