It can be confusing, especially since many Christians do not allow for a difference between mia- and mono-physitism. That we are using English words to stand in for Greek words with technical philosophical meaning that don't really match their standard English meaning only complicates matters.
Mia-, mono-, dyo-physites, and Nestorians all agree that in the Incarnation, the human nature and divine nature came together in Christ. They disagreed on how they came together and what resulted from them coming together. The groups disagree on other matters as well, but in my view these other differences all stem from the primary difference of the understanding the Incarnation.
Mia- and mono- agree that the two natures, divine and human, came together to create a new single nature in Christ. Hence the names mia- and monophysitism. Both mia and mono indicate one in Greek. But they are not synonymous. Mono suggests a unity and simplicity. Mia is a little softer. It allows for a 'one' to be a single union of two things. If you will permit a Scripture reference, Mark 10 has Christ speaking of marriage and divorce saying
For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh’; so then they are no longer two, but one flesh. Therefore what God has joined together, let not man separate.
Here, 'one flesh' is
μία σάρξ (
mia sarx). Two joined into one that within the union still retain their two-ness. Although they are one joined together by God, the two individuals are still two individuals that still have all their original attributes. Thus the Miaphysites speak of Christ's nature. It is a new single nature that is the union of the two natures that retain their two-ness inside the union.
This was not acceptable to Monophysites. The divine nature is just that --- divine. It is infinite. The finite human nature can not be compared to it. Thus when the two natures come together, the divine nature overwhelms the human nature. The common metaphor was that the human nature was like a drop of vinegar disolved in the sea. After the union, both the sea and the vinegar still exist in some sense, but we can also say the vinegar has been dissolved into what is effectively nonexistence. Thus the Monophysites speak of the nature of Christ. Of course the human and divine natures came together in the Incarnation, but the infinite divine nature overwhelmed (or even consumed) the finite nature.
Does that help? Should I address specific points more?