island vs Aegean island

island and Aegean island both are nouns.

Word	Noun	Adjective	Verb	Adverb
island	Yes	No	No	No
Aegean island	Yes	No	No	No

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

Other hyponyms of island include Caribbean Island, barrier island, isle, islet, South Sea Islands.

island (noun)	Aegean island (noun)
a zone or area resembling an island	an island in the Aegean Sea
a land mass (smaller than a continent) that is surrounded by water