A ballplayer is someone who plays baseball. In American English this is the ordinary word for that person, whether they play for money or on a school team. If you hear it with no other sport named, think baseball first. Though actually, in very casual American talk a few people also use it for basketball, because that game uses a ball too — but that is the looser use, not the main one. British English almost always says baseball player instead; ballplayer sounds American. It is a normal everyday word, not fancy and not rude.