Berber vs African

Berber and African both are nouns.

Word	Noun	Adjective	Verb	Adverb
Berber	Yes	No	No	No
African	Yes	Yes	No	No

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

Berber (noun)	African (noun)
a cluster of related dialects that were once the major language of northern Africa west of Egypt; now spoken mostly in Morocco	a native or inhabitant of Africa
a member of an indigenous people of northern Africa

Berber (adjective)	African (adjective)
	of or relating to the nations of Africa or their peoples