baseball vs baseball game

baseball and baseball game both are nouns.

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

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

baseball and 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 synonyms of baseball include ball.

baseball (noun)	baseball game (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