Yes, the motor and trans is both different from a GT to a GTP. It all bolts up the same but a GT transmission will not hold up to any kind of power unless you upgrade it to a HD set-up which the GTP already has.
The motor on the GT is higher compression than the GTP engine, which isn't a bad thing at all really. You would just be putting out more power using the GT motor with less boost than the GTP.