Greek Orthodox vs Orthodox Church

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

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

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

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