Howdy Again
Just been doing a bit of snooping in the Standard Catalog of Smith and Wesson.
It appears that the 38 Military and Police was not cataloged with a 3" barrel. Yes, with S&W we should never say never, but that is how it appears to me. 38 M&P barrel lengths up through the 3rd Change (1915) were pretty well limited to 6 1/2", 6", 5" and 4". Sometime during the 4th Change (1915-1942) 2" barrels were also cataloged.
I have this very funky 2" Post War M&P but I have not dated it. Judging by the speed hammer and the serial number series I'm going to guess it is late 1940s, but that is just a WA guess. I'm pretty sure the grips are older than the gun, they should be on a Smith from about 1904 to 1910.
Standard barrel lengths for the Model 10 (starting in 1957) were 2", 4", 5" and 6". 3" barrels were available by special order 'early on' (what ever that means). 3" barreled Model 10s became catalog items in the 1980s and 1990s. 2 1/2" barrels were made for special contracts.
Moving on to the Model 13, it appears it was available in two standard versions. 3" barrel and round butt or 4" barrel and square butt. The Model 13 was made from 1974 until 1999.
The only Model 13 I have is this 13-2 that I picked up a few years ago.