The S prefix signifies that the gun has an internal hammer block safety. It was used on late WWII and early post war guns. Unfortunately, S&W used it on N and and some K frame revolvers.
You mentioned it’s a .38 special in the title, so that pretty much narrows it down to the N Frame Heavy Duty (shrouded ejector rod) or a K frame .38 Special M&P revolver.
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