I know nothing about anything here. I just keep hearing these terms juggled around in very different but related contexts, and it's all very confusing to me.
Furthermore, how different were the populations of Mycenaean and Classical Greece? (Athens for instance)? Apparently, classical Athenians called the Mycenaean fortress on the Acropolis "Pelasgian". But weren't roughly the same people living there the whole time?
I talked about "Pelasgians" in a thread with is roughly parallel to what you are asking here over here. But in short: there is no such thing. It is a catch-all term which is increasingly useless as we learn more about the pre-Indo-European Aegean. Go to that thread for a good reference book on the topic.
edit: see also here
The Greeks of the Classical period had no knowledge of the past beyond what they made up about the stuff that they saw that was clearly older than they were (e.g. the Mycenaean walls of the Athenian acropolis). They invented a mythical past for themselves. Among these inventions were the "Pelasgians".
Replies of mine that are relevant to your question can be found in these threads: