art history vs liberal arts

art history and liberal arts both are nouns.

Word	Noun	Adjective	Verb	Adverb
art history	Yes	No	No	No
liberal arts	Yes	No	No	No

As nouns, liberal arts is a hypernym of art history; that is, liberal arts is a word with a broader meaning than art history:

art history: the academic discipline that studies the development of painting and sculpture
liberal arts: studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)

Other hypernyms of art history include arts, humanistic discipline, humanities.

art history (noun)	liberal arts (noun)
the academic discipline that studies the development of painting and sculpture	studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)