baseball game vs baseball

baseball game and baseball both are nouns.

Word	Noun	Adjective	Verb	Adverb
baseball game	Yes	No	No	No
baseball	Yes	No	No	No

As nouns, baseball game and baseball are synonyms defined as:

baseball game and baseball: 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 synonyms of baseball game include ball.

baseball game (noun)	baseball (noun)
a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs	a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs
	a ball used in playing baseball