country dancing vs folk dance

country dancing and folk dance both are nouns.

Word	Noun	Adjective	Verb	Adverb
country dancing	Yes	No	No	No
folk dance	Yes	No	Yes	No

As nouns, folk dance is a hypernym of country dancing; that is, folk dance is a word with a broader meaning than country dancing:

country dancing: a type of folk dance in which couples are arranged in sets or face one another in a line
folk dance: a style of dancing that originated among ordinary people (not in the royal courts)

Other hypernyms of country dancing include folk dancing.

country dancing (noun)	folk dance (noun)
a type of folk dance in which couples are arranged in sets or face one another in a line	a style of dancing that originated among ordinary people (not in the royal courts)

country dancing (verb)	folk dance (verb)
	perform a folk-dance