Eutychianism says that the human and divine natures of Christ were combined into one new single (mono) nature: his human nature was "dissolved like a drop of honey in the sea".
Apollinarism or Apollinarianism says that Christ had a human body and human "living principle" but that the Divine Logos had taken the place of the nous, or "thinking principle" . This is analogous but not identical to what might be called a mind in the present day.
After Nestorianism, taught by Nestorius, Archbishop of Constantinople, was refused at the First Council of Ephesus, Eutyches, an archimandrite at Constantinople came up with new views. Monophysitism and Eutyches were also refused at the Council of Chalcedon in 451.
Later, Monothelitism was developed as an attempt to bridge the gap between the Monophysite and the Chalcedonian position, but it too was rejected by the members of the Chalcedonian synod, despite at times having the support of the Byzantine emperors and one of the Popes of Rome, Honorius I. Some are of the opinion that Monothelitism was at one time held by the Maronites, but the Maronite community, for the most part, dispute this, stating that they have never been out of communion with the Catholic Church.
Miaphysitism, the christology of the Oriental Orthodox churches, is sometimes considered a variant of Monophysitism, but these churches view their theology as distinct from Monophysitism and anathematize Eutyches.
Monophysitism Facts for Kids. Kiddle Encyclopedia.