draw poker vs poker game

draw poker and poker game both are nouns.

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

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

draw poker: poker in which a player can discard cards and receive substitutes from the dealer
poker game: any of various card games in which players bet that they hold the highest-ranking hand

Other hypernyms of draw poker include poker.

draw poker (noun)	poker game (noun)
poker in which a player can discard cards and receive substitutes from the dealer	any of various card games in which players bet that they hold the highest-ranking hand