square dance vs country-dance

square dance and country-dance both are nouns.

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

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

square dance: American country dancing in which couples form squares
country-dance: a type of folk dance in which couples are arranged in sets or face one another in a line

Other hypernyms of square dance include contra danse, contradance, contredanse, country dancing.

square dance (noun)	country-dance (noun)
American country dancing in which couples form squares	a type of folk dance in which couples are arranged in sets or face one another in a line

square dance (verb)	country-dance (verb)
dance in formation	perform a contradance