In the end, there can be only one...
We have refactor and refactoring as synonyms. There are 372 total questions (17 unanswered). I think we only need to have one of the two... if we need one at all.
When we post code here, we are obviously looking for a code review, hence no need for a code-review tag (which has already been blacklisted anyway).
But if you went through the front page questions, you'd probably find pretty much all questions are looking for a peer review giving tips to make their code better & cleaner.
We refactor code to enhance readability, to reimplement the functionality to gain in performance, to follow best-practice, ...there are much more specific tags out there already - "refactoring" is basically a side-effect of coming here!
Shall we burninate both?