You have an interesting and somewhat rare gun, Art. The "S" serial number prefix was used for post-war N-frames, the largest revolver frame that S&W made for many years, and only two models of .38 Special were built on the N-frame. Your gun dates from 1948, and is either a .38/44 Heavy Duty or .38/44 Outdoorsman, both the so-called "Transitional" model that was built for a few years after the war when S&W was returning to civilian production.
The Heavy Duty had a fixed rear sight, i.e. milled into the topstrap over the cylinder, and the Outdoorsman had an adjustable rear sight, so you should be able to determine easily which you have. The Heavy Duty eventually (in 1957, when S&W began the model numbering system) became the Model 20 and the Outdoorsman became the Model 23. Both were discontinued in 1966.
The .38/44 was named that because back in the 30s when the gun was introduced S&W was interested in developing a more powerful .38 caliber cartridge, so built a .38 caliber revolver on the beefier .44 Special frame. There was a more powerful .38 Special loading that went along with it, now discontinued, which eventually led to the development of the .357 Magnum.
Only about 2,500 Heavy Duty Transitionals and 2,300 Outdoorsman Transitionals were ever made, so if the gun is in reasonable shape it could be quite valuable, easily upwards of $1,000.