majors vs major league

majors and major league both are nouns.

Word	Noun	Adjective	Verb	Adverb
majors	Yes	No	No	No
major league	Yes	No	No	No

As nouns, majors and major league are synonyms defined as:

majors and major league: the most important league in any sport (especially baseball)

Other synonyms of majors include big league.

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