Are these two cars the same? I know the Lexus IS series is called Toyota Altezza in other countries, so what about these two?

Yes, the only difference is the location of the steering wheel as they are built for different markets (Lexus is for U.S. and Europe, the Toyota is for Japan). Lexus did not reach the Japanese market until 2005, which is why some Lexus models as badged as Toyotas.

The soarers have different engine options as well. They can come with the same 1uzfe 4.0 v8, or the 1jz 2.5 twin turbo inline 6 with a 5spd

Yea these are same, except the location of steering wheel.

on the soarer, most of the gauges are digital. and they of cousre have different badging where the lexus badging would be.