Eastern Orthodox vs Greek Orthodox

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

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

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

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

Other synonyms of Eastern Orthodox include Orthodox, Russian Orthodox.

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

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