Zhuangzi dreamt he was a butterfly that didn't know it was Zhuangzi, and Zhuangzi, upon waking, wondered if he might possibly really be that butterfly now dreaming he is Zhuangzi. But if he is that butterfly, then the butterfly's dream is more authentic than the dream of Zhuangzi since the butterfly in its dreaming is not so sure of its identity as the one dreamt by Zhuangzi.
It's fun to think of these complexities, but they really miss the main point of the story which is that identity is a passing phenomenon to which we need not cling. "Surely, Zhou and a butterfly count as two distinct identities! Such is what we call the transformation of one thing into another." (2:49; Ziporyn)
Lusthaus (Hiding the World in the World, p. 170) picks up on what is most important about this distinction between these two identities, their "nontransference". There is no one identity that changes identities. A meta-Zhuangzi does not transform from Zhuangzi to a butterfly and back again; every identity is discrete and unique. Zhuangzi is only Zhuangzi and the butterfly is only a butterfly; they are not one and the same, but "two distinct identities". But then every identity is also, consequentially, momentary and empty. The point of the story is to shake us lose from our clinging to identity altogether.
Reincarnation, as I understand it, suggests a meta-identity, a "soul", that transmigrates from identity to identity. This is the antithesis of what this story teaches. It is not that Zhuangzi does not entertain the possibility that there is some kind of continuity were an absolute, we are in need of such remedial exercises.
This is convenient for us who do not wish to give up our identity, and thus we spin elaborate schemes wherein we pretend to give it up while simultaneously assuring its perpetuation. "I and the ten thousand things are one" becomes a 'me' that continues as 'one' or 'part of the one'.
Is it saying too much to suggest that death is the end of a particular identity? Yes; we do not, cannot know. Nevertheless, as a therapeutic exercise it seems necessary to say it. It's all good and well to say we "do not know", but until that 'not-knowing' becomes so real in us that we do not cling to identity as if it were an absolute, we are in need of such remedial exercises.
You can check out Scott's writings on Zhuangzi here.