What are the main differences between the Greek Orthodox and Russian Orthodox churches?
As far as doctrine, Holy Tradition, understanding of Scripture, etc., there is no difference between Greek and Russian Orthodox churches. The key word is “Orthodox,” with the ethnic designation in front being a secondary consideration.
Just as in the Roman Catholic confession one may find a “Polish Roman Catholic” parish, an “Italian Roman Catholic” parish, or just a “Roman Catholic” parish—all of which are the same religion but perhaps of different ethnic origins—so too one will encounter “Russian Orthodox” parishes, “Greek Orthodox” parishes, “Romanian Orthodox” parishes, and just “Orthodox” parishes—the latter indicating that the parish is made up of people of various ethnic backgrounds.
Parishes with ethnic designations may employ languages other than English in worship to a greater or lesser degree, or may favor music of one or another national traditions, but the faith is one and the same.