Even the Old Fuff (who never, ever makes a mistake) once got tripped up on this one too.
Smith & Wesson resumed .38 Military & Police production following a short break after World War Two ended, starting on Sept. 12, 1945. They dropped the "V" in the "SV" prefix, but retained the "S" to show that the revolver had the new, positive hammer block safety. The first post-war serial number was S 811,120, starting where they had left off on the "SV" numbers at SV 811,119. The "S" numbers continued until they reached S 999,999 on March 22, 1948
Meanwhile back at the ranch, they decided to resume .38-44 Heavy Duty production (which was built on the larger "N" frame) on June 18,1946, and also used the "S" prefix, but starting at S 62,940. Renamed the Model 24 in 1977, production ended at S 256,133 in 1966.
N-frame revolvers that had an "S" prefix were numbered well below where the K-frame numbers started. Knowing the two ranges of numbers (as explained above) is the only way to avoid confusion.