country-dance vs folk dance

country-dance and folk dance both are nouns.

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

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

country-dance: 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-dance include folk dancing.

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