The Difference between Tewahdo Orthodox Church "Non-Chalcedonian Church"[OO] and Eastern Orthodox [EO] “Chalcedonia Church” are on the following major points.
On the Nature of Christ
During the council of Chalcedon in 451 A.D, the Oriental Orthodox Church had been accused of being 'Monophysite'. Monophysitism meant that in Christ there was only a single nature, the divine nature -humanity of Christ is swallowed up in his divinity . This is NOT what the Oriental Orthodox Church believes/confess. The person who taught that Jesus was basically God with fake human nature was called Eutyches. He is excommunicated from the Church. 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. On the contrary the Eastern Orthodox Churches [used to part of Catholic Church] believe in Dyophysitism (two natures) were understood that they don't believe in the unity between the two natures of Christ. Dyophysitism teaches that, after the union, Christ retained the natures of divinity and humanity in His one Person in such a way that He ate food, slept, laughed, suffered, walked as man in the human nature, but healed the sick and resuscitated Lazarus as God in the divine nature. Thus He is one Person in two natures of humanity and divinity.
On Church Structure
Oriental Orthodox family is governed by its own Patriarch (or equivalent) means each Church has its equivalent Patriarch. Families of the Eastern Orthodox Churches are governed by one Patriarch, who is the Patriarch of Constantinople
The Sign of the Cross - Tewahdo Church do it from Top, bottom, left then right. EO do it from Top, bottom, right then left [Just to be different from Catholic whom they separate from]
Communion - In EO Priest serves the body mixed with the blood. In Tewahdo we do serve separately as it has been done since the Apostolic time.
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