There might be a difference in strength, heat treatment, etc., between the Police Positive and the Police Positive Special, though I certainly don't know that for sure. I don't think the .38 Special was ever available in the Police Positive. The frame opening was likely too short to accommodate a cylinder long enough to handle the .38 Special cartridge. The only one I've had any experience with in .38 Special was a Police Positive Special.
Still probably not a good idea to use a cartridge for which a gun was not designed.