On guns that typically came with target stocks that covered the base of the butt, they would stamp the serial number in the crane.
This is typically true, but the number on the butt should always
First, many postwar guns wearing oversize Target stocks did not ship with these stocks originally; they were added by a former owner.
Second, there are numerous S&Ws floating around with incorrect numbers inside the yoke cut, and I used to own one of them- a Model 19-5. It appeared to have been built with an "8" inside the yoke cut where there was supposed to be a "9"; a factory inspector apparently caught the error and attempted to correct it by overstamping the bad digit with a "9", but since the two numbers are so similar in shape, the correction did NOT make things much clearer.
In cases where the numbers do not match, the number on the butt or frontstrap is treated as definitive.
ALWAYS check the butt or frontstrap!