ballroom dance vs ballroom dancing

ballroom dance and ballroom dancing both are nouns.

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

As nouns, ballroom dance and ballroom dancing are synonyms defined as:

ballroom dance and ballroom dancing: any of a variety of social dances performed by couples in a ballroom

ballroom dance (noun)	ballroom dancing (noun)
any of a variety of social dances performed by couples in a ballroom	any of a variety of social dances performed by couples in a ballroom