major league vs majors

major league and majors both are nouns.

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

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

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

Other synonyms of major league include big league.

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