baseball player vs ballplayer

baseball player and ballplayer both are nouns.

Word	Noun	Adjective	Verb	Adverb
baseball player	Yes	No	No	No
ballplayer	Yes	No	No	No

As nouns, baseball player and ballplayer are synonyms defined as:

baseball player (noun)	ballplayer (noun)
an athlete who plays baseball	an athlete who plays baseball