Egyptian vs Afro-Asiatic

Egyptian and Afro-Asiatic both are nouns.

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

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

Egyptian: the ancient and now extinct language of Egypt under the Pharaohs; written records date back to 3000 BC
Afro-Asiatic: a large family of related languages spoken both in Asia and Africa

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

Egyptian (noun)	Afro-Asiatic (noun)
the ancient and now extinct language of Egypt under the Pharaohs; written records date back to 3000 BC	a large family of related languages spoken both in Asia and Africa
a native or inhabitant of Egypt

Egyptian (adjective)	Afro-Asiatic (adjective)
of or relating to or characteristic of Egypt or its people or their language