Normally, a "refresh" refers to a styling update without any meaningful changes to the underlying design and structure of the vehicle (underneath the "skin"). Example, the 2011 Chrysler 200 is a "refresh" of the previous Chrysler Sebring. The 2010 Ford Mustang is a "refresh" of the 2005 - 2009 model.
A "redesign" (or a "re-engineering") normally means a more thorough rework in which the underlying structure is changed, suspension attachment points are changed, sometimes the design of the suspension itself is changed, the crash structures change, etc. For example, the VW Golf Mk5 (2005/2006 onward) might bear a family appearance resemblance to its predecessor, the Mk4 (1999 - 2005) but it is entirely different underneath. Suspension, wiring harness, underbody structure, etc are all different.