Colt made a version of their Gold Cup target model in .38 Special (wadcutter). It was different in that the action was straight-blowback and the chamber was threaded to grip the fired case more tightly and slow the backward movement of the slide. Colt also made kits for military match units and civilian gunsmiths that consisted of a conventional (locked breech) top unit (slide, barrel, and the rest) designed for the purpose of converting a .38 Super or .45 to .38 Special.
Being long and rimmed, .38 wadcutters didn't always feed reliably in automatic pistols, and when bullseye shooters turned to using their .45 pistols in the center fire match(s) the market for these guns largely dried up.
One interesting sidelight to all of this was the development of the .38 AMU cartridge, that consisted of a .38 Special body with a .9mm head - in other words rimless - in an attempt to solve some of the feeding problems.