waltz vs ballroom dancing

waltz and ballroom dancing both are nouns.

Word	Noun	Adjective	Verb	Adverb
waltz	Yes	No	Yes	No
ballroom dancing	Yes	No	No	No

As nouns, ballroom dancing is a hypernym of waltz; that is, ballroom dancing is a word with a broader meaning than waltz:

waltz: a ballroom dance in triple time with a strong accent on the first beat
ballroom dancing: any of a variety of social dances performed by couples in a ballroom

Other hypernyms of waltz include ballroom dance.

waltz (noun)	ballroom dancing (noun)
a ballroom dance in triple time with a strong accent on the first beat	any of a variety of social dances performed by couples in a ballroom
music composed in triple time for waltzing
an assured victory (especially in an election)

waltz (verb)	ballroom dancing (verb)
dance a waltz