Egyptian vs Cairene

Egyptian and Cairene both are nouns.

Word	Noun	Adjective	Verb	Adverb
Egyptian	Yes	Yes	No	No
Cairene	Yes	No	No	No

As nouns, Cairene is a hyponym of Egyptian; that is, Cairene is a word with a more specific, narrower meaning than Egyptian:

Other hyponyms of Egyptian include Copt, Theban, Nubian.

Egyptian (noun)	Cairene (noun)
the ancient and now extinct language of Egypt under the Pharaohs; written records date back to 3000 BC	a native or inhabitant of Cairo
a native or inhabitant of Egypt

Egyptian (adjective)	Cairene (adjective)
of or relating to or characteristic of Egypt or its people or their language