square dancing vs contra danse

square dancing and contra danse both are nouns.

Word	Noun	Adjective	Verb	Adverb
square dancing	Yes	No	No	No
contra danse	Yes	No	Yes	No

As nouns, contra danse is a hypernym of square dancing; that is, contra danse is a word with a broader meaning than square dancing:

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

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

square dancing (noun)	contra danse (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 dancing (verb)	contra danse (verb)
	perform a contradance