ball club vs baseball club

ball club and baseball club both are nouns.

Word	Noun	Adjective	Verb	Adverb
ball club	Yes	No	No	No
baseball club	Yes	No	No	No

As nouns, ball club and baseball club are synonyms defined as:

ball club and baseball club: a team of professional baseball players who play and travel together

Other synonyms of ball club include club, nine.

ball club (noun)	baseball club (noun)
a team of professional baseball players who play and travel together	a team of professional baseball players who play and travel together