Berber vs Afro-Asiatic

Berber and Afro-Asiatic both are nouns.

Word	Noun	Adjective	Verb	Adverb
Berber	Yes	No	No	No
Afro-Asiatic	Yes	No	No	No

As nouns, Afro-Asiatic is a hypernym of Berber; that is, Afro-Asiatic is a word with a broader meaning than Berber:

Berber: a cluster of related dialects that were once the major language of northern Africa west of Egypt; now spoken mostly in Morocco
Afro-Asiatic: a large family of related languages spoken both in Asia and Africa

Other hypernyms of Berber include Afrasian, Afrasian language, Afroasiatic, Afroasiatic language, Hamito-Semitic.

Berber (noun)	Afro-Asiatic (noun)
a cluster of related dialects that were once the major language of northern Africa west of Egypt; now spoken mostly in Morocco	a large family of related languages spoken both in Asia and Africa
a member of an indigenous people of northern Africa