I load for both the 17 Rem and 17-222 Mag. and can assure you they are not the same cartridge, as the 17 Rem. has less capacity, a longer neck and shorter case length, but as noted in the link the 17 Rem. is longer than the 223 case.
Curious, why you would spend that much time forming 17 Rem brass from 204 cases when you can buy 17 Rem brass new? Isn't that why too much time at the loading bench?