round dancing vs round dance

round dancing and round dance both are nouns.

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

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

round dancing and round dance: a ballroom dance characterized by revolving movement

round dancing (noun)	round dance (noun)
a ballroom dance characterized by revolving movement	a folk dance; dancers form a circle
	a ballroom dance characterized by revolving movement