The 9X23 is tapered and loaded to higher pressure (55,000) than the straight walled 38 Super (36,500 psi).
Their overall length is essentially/nearly/almost the same as they are intended for the same sized gun.
Converting a 38 Super gun to 9X23 is fairly simple. Just need a new barrel. Extractor might or might not need adjustment. A stronger recoil spring might be desirable.