Are there theological differences between the Greek Orthodox church and the Coptic (Egyptian) Orthodox church? Is there a theological difference between the Greek Orthodox church and the Coptic (Egyptian) Orthodox church?
The basic between the two is over the Christological definition accepted at the Council of Chalcedon in 451, where Christ was recognized as being worshiped both 'in' two natures that exist 'inconfusedly, unchangeably, indivisibly, inseparably'. The Copts and other miaphysites believed that this definition was ambiguous and could be understood in a Nestorian manner. They preferred to speak of Christ being worshiped in one human-divine nature 'out of' two natures. Much of the difficulty here arises from the ambiguity of the term 'nature'-- is it a particular, in the manner the Nestorians used it (equivalent to hypostasis) or a universal (equivalent to 'ousia', essence)? If it is the former, then the story of the Incarnation is the story of the Word of God uniting to a particular human being named Jesus at the moment of his conception, which is in fact how Nestorius and his followers understood the incarnation. If 'nature' is a universal, however, then the Incarnation is the story of the Word of God uniting with human nature and becoming Jesus. That is, in this theology, the person of Jesus is identical to the person of the Word of God who has taken on humanity, not a person who is somehow united to the Word. In any case, the Second Council of Constantinople of 553 affirms the latter narrative as the understanding of the Incarnation accepted by the Greeks as well.

So, at this point, the differences between Coptic and Greek theology become a very subtle game of parsing technical language. However, the Copts do not officially accept any of the ecumenical councils accepted by the Greeks, from Chalcedon on. This leads to the often-overlooked theological difference of Copts speaking of one will in Christ while Greeks, following the Third Council of Council of Constantinople of 680-681, speak of two wills in Christ, human and divine in perfect harmony.