four-hitter vs baseball game

four-hitter and baseball game both are nouns.

Word	Noun	Adjective	Verb	Adverb
four-hitter	Yes	No	No	No
baseball game	Yes	No	No	No

As nouns, baseball game is a hypernym of four-hitter; that is, baseball game is a word with a broader meaning than four-hitter:

four-hitter: a game in which a pitcher allows the opposing team 4 hits
baseball game: a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs

Other hypernyms of four-hitter include ball, baseball.

four-hitter (noun)	baseball game (noun)
a game in which a pitcher allows the opposing team 4 hits	a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs