ball club vs baseball team

ball club and baseball team both are nouns.

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

As nouns, baseball team is a hypernym of ball club; that is, baseball team is a word with a broader meaning than ball club:

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

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