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The Wikipedia article on Monophysitisism answers your question when it says:
There are two major doctrines that can indisputably be called "monophysite":
- Eutychianism holds that the human and divine natures of Christ were fused into one new single (mono) nature: His human nature was "dissolved like a drop of honey in the sea".
- Apollinarism or Apollinarianism holds 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", analogous but not identical to what might be called a mind in the present day.
In other words, Eutychianism is a subset of Monophysitisism.