Okay, let me see if I got this, combining everything that everyone has said. Catholic orthodoxy teaches that Christ is one person who has two natures, that Christ is fully divine and fully human, and that these natures are not separate from each other. For example, The human nature is not a husk that the divine nature fills (which is what Nestorius taught).
The Nestorians divided the two natures of Christ so far, that they became two persons, so that the God person of Christ did not suffer and die upon the Cross, only the human person. This interferes with the atonement. It also means that the Nestorians denied that Mary is Theotokos.
Do I have it right? Please make corrections where necessary.
I have a few follow up questions.
In Catholic Orthodoxy, are the two natures of Christ so close that they are blended? It seems to me that if that were so, that he would no longer be God and man, but some third kind of being.
Also, the Oriental Orthodox Churches left at Chalcedon. It is said that they are monophysite. Mono means one. Do the Oriental Orthodox believe an opposite heresy to Nestorianism? That Christ only has one nature?