For most of their separate history, the Chalcedonian churches called their Oriental Orthodox counterparts monophysite, a term that in Greek suggests Christ has only a single, effectively divine nature with his humanity absorbed or dissolved into it, the actual heresy of Eutyches that both Chalcedon and Cyril himself had opposed. The Oriental Orthodox churches have long rejected the label as a caricature, insisting their own position, better rendered miaphysite, one united nature rather than a single simple nature, never denied Christ's full and complete humanity, only refused to speak of it as a separate nature alongside his divinity.
Sustained modern ecumenical dialogue, particularly a series of unofficial and later official conversations between Eastern Orthodox and Oriental Orthodox theologians from the 1960s onward, has concluded that the two families largely mean the same thing by different technical vocabulary, Chalcedonian two-natures language on one side and Cyrilline one-nature language on the other, both intending to affirm Christ as fully God and fully human in a single, undivided person. Several joint statements have declared the underlying faith to be substantially shared.
Formal reunion has not followed the theological agreement, since centuries of separate liturgical, canonical and jurisdictional development stand alongside the Christological question, but the modern consensus has meaningfully changed how each side now describes the other, from heretic to estranged sibling.