Hi there...
Fellow Corolla owner here. I currently own/drive a 2005 Toyota Matrix TRD. It is a cross between a Corolla 5 door and a Corolla Wagon (Estate). It's powered by a 1ZZFE 1.8L VVTi 130HP engine. 5 Speed manual. The TRD Edition is a Canadian-only model. It includes specific 17" aluminum alloys, TRD exhaust tip, rear spoiler, fog lights, TRD Shift Knob, Panasonic AM/FM/CD/MP3 Player. No power windows, but strangely enough it has power door locks.
The Toyota Matrix was produced from 2002 (as a 2003 model) til 2007 (as a 2008 model). The replacement 2009 Matrix which has been totaly redesigned just came out this month. It is similar to the European Auris or your current Corolla 5 door. I believe that they share the same platform but the styling once again is unique to north America... See below.
TRDfrankie