ballroom dancing vs ballroom dance

ballroom dancing and ballroom dance both are nouns.

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

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

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

ballroom dancing (noun)	ballroom dance (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