What's the difference between Eastern Orthodox and Greek Orthodox?
Theologically, none. Different Orthodox Churches have their own cultural and historical markers, language, slight variations of vestments, even external praxis and non-canonical parts of the Divine Liturgy (for example, the Greeks don't use the Beatitudes in the Third Antiphon).
The reason why all Orthodox can commune in any Orthodox church, regardless which Patriarchy they are from, is because all particular Churches that form the Orthodox Church community profess the same faith. Communion is the expression of, and not a means of establishing, theological union.