Answer
The terms miaphysitism and dyophysitism are used to explain the nature of the incarnation and how Jesus should be thought of as both God and man.
Dyophysitism is the position that Jesus is one person of one substance but with two different natures: one divine and one human. This term is from the Greek duo for “two” and physis for “nature.”
Miaphysitism is the position that Jesus is one person of one substance with only one, fully integrated nature that is both fully human and fully divine. This term is from the Greek mia for “one” and physis for “nature.”
The real difference comes down to whether Christ has two natures or one. The issue is not whether Christ is fully God and fully human, but in what way He is both. The Bible never explicitly answers these questions, but Bible-believing Christians try to find the position that best accounts for all of the biblical evidence. Also, each of these positions has implications that need to be addressed. It helps to understand miaphysitism and dyophysitism in contrast to each other and in relation to some other views.
Apollonarius, who became bishop of Laodicea in 361, taught that Jesus had a human body and a divine nature, without a human mind or spirit. However, this would make Jesus something other than a genuine human, and Apollinarianism was rejected by the Council of Alexandria in 362 and the Council of Constantinople in 381.
Another position put forward was that of Nestorius, who became bishop of Constantinople in 428. This position states that Jesus had two natures so divided that He was actually two persons. However, this position was rejected, as Scripture is clear that Jesus is only one person and there is no indication that a human Jesus did anything independently of a divine Jesus or vice versa.
Another position, the monophysite position, also called Eutychianism after Eutyches, a church leader who lived 378—454, states that Jesus had one nature in which the human nature was fully absorbed by the divine nature and essentially became a third kind of nature. So, Jesus’ nature was more than human, but less than divine. A variation on this is that Jesus’ human nature was completely absorbed into his divine nature, so that only the divine nature remained. This would be similar to Apollinarianism, mentioned above.
The orthodox position finally formulated at the Council of Chalcedon in 451 tried to account for all of the biblical data. The council stated that Jesus is one person with two natures—one divine and one human. He is genuinely human and genuinely divine. Jesus exhibits characteristics of both. He can be exhausted, asleep in the boat, and then be awakened and command the storm to be still (Mark 4:37–41). He can be tempted yet not sin (Hebrews 4:15).
Some will lump monophysitism and miaphysitism together. However, non-Chalcedonian churches today who officially hold to miaphysitism (a number of Eastern Orthodox churches) say they affirm that Jesus is fully divine and fully human in His nature and that their differences with dyophysites are merely semantic.
Some Christian theologians get much exercised about differences like these. For the average Christian in modern times, such questions and distinctions may seem insignificant, if not mind-numbing. At times, theologians may delve more deeply into areas of mystery and draw dogmatic conclusions that may reach beyond the straightforward propositions of Scripture. Likewise, sometimes ordinary Christians do not care about the more difficult implications of theological positions and formulations in favor of simply “I love Jesus” or “Jesus loves me.” Both errors should be avoided. We should care deeply about these things without being dogmatic where Scripture has not given us clear statements.
Scripture does not directly address whether Jesus had two natures or one, fully integrated nature that did not confuse or dilute His human or divine qualities. In some cases, it may come down to semantics. If miaphysites affirm the full deity and full humanity of Jesus and also affirm that in His death He was an adequate representative of the human race so that He could atone for our sins as the second Adam (Romans 5:12–20), then it would seem that they are thoroughly orthodox in this area, even though their position is close to (and often equated with) one that has been deemed heretical. In other instances, if one’s position leads to implications that are clearly unbiblical (denying either the humanity or deity of Christ, thus denying His ability to represent us on the cross), then the charge of heresy is warranted.