The only model ever made in .32-20 was the prewar M&P -- same gun as the .38 Special M&P, but differently chambered. S&W stopped production just before WWII and never reintroduced the .32-20 chambering after the war. Just under 150,000 were produced over four decades. These were K-frame revolvers.
The .32 Long was offered both on the small I-frame (hundreds of thousands made) and on the mid-size K-frame, of which only a few thousand were made; most of the K-frame .32s had adjustable sights. With some special order exceptions, K-frame .32 Long Production is limited to just before WWII (only a few dozen made) and the first two postwar decades (production less than 4,000).
The gun you saw would be a .32 Hand Ejector, an I-frame revolver. If it had square butt stocks, it would have been marketed as a .32 Regulation Police, a variety of the .32 Hand Ejector with slightly larger stocks. The RP was introduced in 1917. For the first several years of production, RPs had a patent date (June 5, 1917) stamped on the bottom of one wooden panel.
After the war, J-frame .32s were produced for several decades. I think you can still get J-frame revolvers chambered in 32 H&R Magnum or .327 Federal. These will also shoot .32 Long, but the guns are not limited to the shorter, older round.