Welcome to the forums from the cotton and peanut covered plains of the Wiregrass! You have a .32 Winchester Model Military & Police revolver, Model 1902 made around 1905. It went back to S&W for work in August 1921 and received a refinish in blue and probably received a new barrel. I say that because the caliber stamp is .32-20 CTG and that was not used until around 1921-22. Your barrel should be stamped .32 Winchester if original. These gun were not popular and S&W stopped producing them around 1930 and sold them out of inventory until it was depleted by 1940.