passing game vs football play

passing game and football play both are nouns.

Word	Noun	Adjective	Verb	Adverb
passing game	Yes	No	No	No
football play	Yes	No	No	No

As nouns, football play is a hypernym of passing game; that is, football play is a word with a broader meaning than passing game:

passing game: (American football) a play that involves one player throwing the ball to a teammate
football play: (American football) a play by the offensive team

passing game (noun)	football play (noun)
(American football) a play that involves one player throwing the ball to a teammate	(American football) a play by the offensive team