The SE doesn't have that ending. There's technically 3 versions:
- Theatrical
- SE
- Super-Extended SE
The "SEE" is basically just an Easter Egg on the UE DVD. It contains the scene of the T-1000 "searching" John's room that's cut out of both of the other versions, and the "flash-forward" ending. I've heard it's also included on the "Skynet Edition" Blu-Ray as well. The "Extreme Edition" has the regular SE without these two scenes as the default version, and the theatrical version as an Easter Egg.
And on further reflection, I'd also keep the SE scene of the T-1000 killing Max the dog and discovering that its name was not, in fact, Wolfie.