Zambian vs African

Zambian and African both are nouns.

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

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

Zambian (noun)	African (noun)
a native or inhabitant of Zambia	a native or inhabitant of Africa

Zambian (adjective)	African (adjective)
of or relating to or characteristic of Zambia or its people	of or relating to the nations of Africa or their peoples