three-card monte vs card game

three-card monte and card game both are nouns.

Word	Noun	Adjective	Verb	Adverb
three-card monte	Yes	No	No	No
card game	Yes	No	No	No

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

three-card monte: a gambling card game of Spanish origin; 3 cards are dealt face up and players bet that one of them will be matched before the others as the cards are dealt from the pack one at a time
card game: a game played with playing cards

Other hypernyms of three-card monte include cards.

three-card monte (noun)	card game (noun)
a gambling card game of Spanish origin; 3 cards are dealt face up and players bet that one of them will be matched before the others as the cards are dealt from the pack one at a time	a game played with playing cards