If you look at the full name of an STi, it's Impreza WRX STi. The STi wording is Subaru Technica International, kind of like SVT is to Ford or Nismo to Nissan.

The STi version of the Impreza is loads better than the WRX. You get a stronger transmission with better differentials (and a limited slip front diff), you get better brakes, better suspension setup with stiffer bushings. The motor is better (especially when comparing 08+ WRX vs 08+ STi). The turbo is larger when you look at 02-08 WRX vs 04-07 STi. The intercooler is larger also larger on the STi. The wheel bearings on 05+ STi's are much better than what is offered for the WRX and there is a larger supply of wheels to choose from in the sense that there are more wider wheels available outside of Rota.

I'm sure there is plenty more that I'm leaving out.