refactor vs. rewrite

[http://dummy.us.eu.org/robert (Robert)]

I think of "rewrite" is completely re-implementing a program or a system,
in perhaps a different language but also possibly using a completely
different set of libraries or modules.

I think of "refactor" is when smart parts of a program are re-implemented,
perhaps in a different language (using a bridge or foreign interface).

Maybe I'm making a distinction without a difference, however.
🤷