ballplayer vs player

ballplayer and player both are nouns.

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

As nouns, player is a hypernym of ballplayer; that is, player is a word with a broader meaning than ballplayer:

Other hypernyms of ballplayer include athlete, jock, participant.

ballplayer (noun)	player (noun)
an athlete who plays baseball	a theatrical performer
	a person who participates in or is skilled at some game
	someone who plays a music as a profession
	a person who pursues a number of different social and sexual partners simultaneously
	someone who takes part in an activity