forward pass vs passing game

forward pass and passing game both are nouns.

Word	Noun	Adjective	Verb	Adverb
forward pass	Yes	No	No	No
passing game	Yes	No	No	No

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

forward pass: a pass to a receiver downfield from the passer
passing game: (American football) a play that involves one player throwing the ball to a teammate

Other hypernyms of forward pass include pass, passing, passing play.

forward pass (noun)	passing game (noun)
a pass to a receiver downfield from the passer	(American football) a play that involves one player throwing the ball to a teammate