majors vs conference

majors and conference both are nouns.

Word	Noun	Adjective	Verb	Adverb
majors	Yes	No	No	No
conference	Yes	No	No	No

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

majors: the most important league in any sport (especially baseball)
conference: an association of sports teams that organizes matches for its members

Other hypernyms of majors include league.

majors (noun)	conference (noun)
the most important league in any sport (especially baseball)	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