Refactoring and rewriting are very similar in effect - often refactoring involves rewriting. I believe the difference is in the intent and the scale: refactoring is the intent to improve code, from the smallest scale up - single statement, block or sub. Rewriting tends to be more of a "start again" approach to fixing something, and usually applied to a scale larger than a statement or block.

I believe both terms can be used most of the time, but there are folks who strongly believe in XP who have a special meaning for the word refactoring, that implies more than the mere language definition.