supper club vs night club

supper club and night club both are nouns.

Word	Noun	Adjective	Verb	Adverb
supper club	Yes	No	No	No
night club	Yes	No	No	No

As nouns, night club is a hypernym of supper club; that is, night club is a word with a broader meaning than supper club:

supper club: usually a small luxurious nightclub
night club: a spot that is open late at night and that provides entertainment (as singers or dancers) as well as dancing and food and drink

Other hypernyms of supper club include cabaret, club, nightclub, nightspot.

supper club (noun)	night club (noun)
usually a small luxurious nightclub	a spot that is open late at night and that provides entertainment (as singers or dancers) as well as dancing and food and drink