Is the Coptic Orthodox Church in communion with the Greek and Russian Orthodox Church? If not, what are their differences?
The Coptic Orthodox Church (Non-Chalcedonian Church) is not in full communion with the Greek and the Russian Orthodox Churches (Chalcedonian).
During the council of Chalcedon, the Coptic Orthodox Church had been accused of being 'Monophysite'. The term monophysite comes from two Greek words meaning "single nature". Monophysitism merged Christ's humanity into His divinity so that effectively it meant that in Christ there was only a single nature, the divine nature. This is NOT what the Coptic Orthodox Church believes. We believe that "Christ's divinity parted not from His humanity not for a single moment nor a twinkling of an eye" and we recite this statement in every liturgy. So we are Miaphysite and not Monophysite. Miaphysitism (one nature) means that the Lord Jesus Christ is perfect human and perfect divine and these two natures are united together without mingling, without confusion, and without alteration in one nature; the nature of God incarnate.
Also the Eastern Orthodox Churches who believe in Diophysitism (two natures) were understood that they don't believe in the unity between the two natures of Christ. In the recent dialogue, the Eastern Orthodox Churches confessed their belief in the union of the two natures according to the words of St. Cyril of Alexandria Miaphysis 'tou theo tou logo se sarkomeeni' which means one nature for the incarnated Logos of God.
Today there are many dialogues to resolve these differences and misunderstanding. More information about the current dialogues regarding the unification of the churches can be found at these websites