Your picture makes it clear what you have. The closest SN I have on my list is SN 72535 which shipped from the factory in 10/1917. Yours will be close to that date. S&W cataloged it as the .32-20 Military and Police (M&P) Model, square butt. The grips appear to be altered from the type used by S&W during the 1920s and would not be original for that date. .32-20 and .32 WCF (Winchester Center Fire) are two names for the same cartridge. Earlier revolvers of the same type and caliber were caliber stamped on the barrel as "32 Winchester CTG." CTG is simply an abbreviation for Cartridge.
If you plan to shoot it, be aware that factory loaded .32-20 ammunition has become a somewhat scarce and expensive cartridge in recent years and may be difficult to find. Due to the logistical difficulty of finding ammunition, most .32-20 revolver shooters reload their own ammunition. New brass cases are sometimes available.
S&W stopped making the K-frame .32-20 M&P in the late 1920s. Essentially the same revolver chambered in .38 Special is still around. Only around 144K .32-20 K-frames were ever made by S&W, compared to many millions made of much the same revolver chambered in .38 Special.
Hope this information helps you.