Greek Orthodox vs Eastern Orthodox

Greek Orthodox is not a noun while Eastern Orthodox is a noun.

Word	Noun	Adjective	Verb	Adverb
Greek Orthodox	No	Yes	No	No
Eastern Orthodox	Yes	Yes	No	No

As adjectives, Greek Orthodox and Eastern Orthodox are synonyms defined as:

Greek Orthodox and Eastern Orthodox: of or relating to or characteristic of the Eastern Orthodox Church

Other synonyms of Greek Orthodox include Orthodox, Russian Orthodox.

Greek Orthodox (noun)	Eastern Orthodox (noun)
	derived from the Byzantine Church and adhering to Byzantine rites

Greek Orthodox (adjective)	Eastern Orthodox (adjective)
of or relating to or characteristic of the Eastern Orthodox Church	of or relating to or characteristic of the Eastern Orthodox Church