Refactoring vs Redesign??? or Restructuring

Is it refactoring or a redesign?
Its a 'big refactoring'.
We spent the last two weeks on refactoring.
You guys are doing redesign and calling it as refactoring.

I am sure that most of us would have come across questions/statements like the above on various occassions. The above statements initially gave me a sense that its the magnitude of the change that differentiates between a refactoring and redesign.

Last evening I had a chance to chat with Martin Fowler regarding this and here is Martin's words.
"Rather than Refactoring vs Redesign I would like to see it Refactoring vs Restructuring. Refactoring is one of the ways to restructure your code. You can restructure your code by rewriting a class also. Refactoring is my preferred way of restructuring. While each transformation(refactoring) will result in a small change, a sequence of transformations(refactorings) can produce a significant restructuring.".

More about refactoring can be found here.