.32-44 was a target cartridge specifically for a large frame S&W top-break revolver built on the #3 frame.
There are 2 very different .38-44 cartridges. The early one is for the #3 Target and loaded with black powder and comments for the .32-44 apply to this one too. Both of these must be hand-loaded and correct brass is not available!
The second .38-44, introduced ca.1929, is nothing more than the .38 Special loaded to significantly higher pressure, around 25,000 PSI or higher. It was originally intended as a Police Service cartridge and chambered in a gun built on the 3rd Model .44 Hand Ejector frame, hence the .38-44 designation. These were the .38-44 Heavy Duty and .38-44 Outdoorsman. The difference being fixed or target sights respectively. Since it is a simply a .38 Spl. it is a much simpler proposition to hand load, but hand loaded it must be as factory loads have not been available since the 1960s or shortly thereafter. Published velocities for factory ammunition when it was available range from 1115-1150 FPS with the 158 gr. RN bullet, either lead or copper-capped lead. Proper bullets, the 158 gr. capped round-nose with lead bearing surface, have not been available to hand loaders for many years.
Gunsmithing S&W since 1961