rummy vs card game

rummy and card game both are nouns.

Word	Noun	Adjective	Verb	Adverb
rummy	Yes	Yes	No	No
card game	Yes	No	No	No

As nouns, card game is a hypernym of rummy; that is, card game is a word with a broader meaning than rummy:

rummy: a card game based on collecting sets and sequences; the winner is the first to meld all their cards
card game: a game played with playing cards

Other hypernyms of rummy include cards.

rummy (noun)	card game (noun)
a card game based on collecting sets and sequences; the winner is the first to meld all their cards	a game played with playing cards
a chronic drinker

rummy (adjective)	card game (adjective)
beyond or deviating from the usual or expected