basketball league vs conference

basketball league and conference both are nouns.

Word	Noun	Adjective	Verb	Adverb
basketball league	Yes	No	No	No
conference	Yes	No	No	No

As nouns, conference is a hypernym of basketball league; that is, conference is a word with a broader meaning than basketball league:

basketball league: a league of basketball teams
conference: an association of sports teams that organizes matches for its members

Other hypernyms of basketball league include league.

basketball league (noun)	conference (noun)
a league of basketball teams	a discussion among participants who have an agreed (serious) topic
	a prearranged meeting for consultation or exchange of information or discussion (especially one with a formal agenda)
	an association of sports teams that organizes matches for its members