Does saying "states of definite mass" is the same as saying "mass eigenstates"?
Usually yes, but it would be good form to reference the text you are reading to provide us with enough information to answer your question.
I read this from Wikipedia
" Neutrino oscillation arises from a mixture between the flavor and mass eigenstates of neutrinos. That is, the three neutrino states that interact with the charged leptons in weak interactions are each a different superposition of the three neutrino states of definite mass. "
Yes, they are the same.
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