Dare I presume to not only summarize the EO response, but also the OO response? Please, anyone correct me if I speak incorrectly.
The Eastern Orthodox (Chalcedonian) doctrine is dyophysitism. Christ is two natures (one divine, one human) but that these are united inseparably in the one person of Jesus Christ. He is fully man and fully God.
The Oriential Orthodox (Non-Chalcedonian) doctrine is miaphysitism. Christ is one united nature (a single nature that is human and divine), and these are in the one person of Jesus Christ. He is fully man and fully God.
What the actual difference is, result wise, can be confusing. Honestly, our churches aren't sure. Several joint statements have been made in the last several decades affirming that these doctrines are the same, only the language used to express them is different. We mean the same thing, we're just saying it differently.
Our churches remain in dialogue on the theological and historical issues of the Council of Chalcedon, with the possibility of reunification.