I'm not certain, but I think in the US they just called it a Corolla. I know that the one my boss had was badged SR5 on the rear of the hatch, but the owner's manual said "Corolla SR5/GTS" or something along those lines (it was a long time ago!) I went with him when he was shopping for a car, and the Toyota salesman did a great job, he sat him in an MR2 first and then the SR5 with a sun roof seemed like a great deal
He totalled the car in its second year, taking a tight highway exit much too fast.