round dance vs ring dance

round dance and ring dance both are nouns.

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

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

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