[JTM45]

The 2001 model looks identical to the 2002 model, but are they the same?

It should be identical. The only thing that's ever changed on that guitar is the Lo-Pro Edge was changed to an Edge-Pro in 2003.
You've definitely got the better one of the two, as long as you're not one of the 0.05% of people who prefers the Edge-Pro,lol.

Nice guitars!