hockey league vs conference

hockey league and conference both are nouns.

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

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

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

Other hypernyms of hockey league include league.

hockey league (noun)	conference (noun)
a league of hockey 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