No, it isn't plagiarism, nor even self-plagiarism, which is a bit different.
Plagiarism is claiming that something you write was created by yourself when you copy it without attribution to the real originator. It doesn't actually need to be a faithful (cut-paste) copy. Rephrasing is enough for it to be plagiarism. If you claim it for your own when it isn't, that is plagiarism. It is a kind of stealing.
But your earlier version is yours, so no plagiarism.
Self-plagiarism is a bit different and has a different purpose. If you write something and publish it, then, in the future if you want to copy from it in another publication, you should cite the original just as if it was written by another. The reason is that readers of your new work will want to trace back the ideas you present to their earlier form, so as to get a more complete context of the ideas. Copying your own published work without citing it prevents this chain of research to occur, so is considered wrong.
But you haven't published the first version, so there is no reason to even cite it. You can just copy. It is really just a new version of a work in progress.