baseball club vs ball club

baseball club and ball club both are nouns.

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

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

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

Other synonyms of baseball club include club, nine.

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