major-league club vs major-league team

major-league club and major-league team both are nouns.

Word	Noun	Adjective	Verb	Adverb
major-league club	Yes	No	No	No
major-league team	Yes	No	No	No

As nouns, major-league club and major-league team are synonyms defined as:

major-league club and major-league team: a team that plays in a major league

major-league club (noun)	major-league team (noun)
a team that plays in a major league	a team that plays in a major league