stud poker vs poker game

stud poker and poker game both are nouns.

Word	Noun	Adjective	Verb	Adverb
stud poker	Yes	No	No	No
poker game	Yes	No	No	No

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

stud poker: poker in which each player receives hole cards and the remainder are dealt face up; bets are placed after each card is dealt
poker game: any of various card games in which players bet that they hold the highest-ranking hand

Other hypernyms of stud poker include poker.

stud poker (noun)	poker game (noun)
poker in which each player receives hole cards and the remainder are dealt face up; bets are placed after each card is dealt	any of various card games in which players bet that they hold the highest-ranking hand