ballplayer vs baseball player

ballplayer and baseball player both are nouns.

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

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

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