I agree with "refactoring is a fancy word for clean up your code" but not with "just". People use fancy words for a reason: sometimes because they want to look clever, and sometimes because they're conveying a greater or more precise meaning, and IMHO refactoring (even if occasionally misused) is generally referring to the latter.
"Clean up" could mean anything from "reformatting a bit" to "rewriting large chunks".
"Refactoring" means specifically something like "small incremental changes to the code, designed to maintain the same functionality, while transforming it into a better design". And there's a body of best practice on the sort of things you do: some is ad-hoc, but there are general principles, like using unit tests, extracting part of functions into new functions or classes, etc, which people can and should learn.
You say "just trick management into allocating time for code clean up". But if saying "refactoring" correctly conveys the concept that a steady investment in clarity now will pay dividends in efficiency in the future, then that's not a "trick", that's clear and effective communication.