Simply the factory identification number...the number on the 'Job card' as it went through the works...Really a quality control and rectification number prior to final assembly.
BSA stamped engine & frame numbers at different times during the manufacturing process over the years.
Engine casings were generally stamped with the model number only so the assembly workers would know what parts should be put in it,
This is why the WM20 is all over the place and may be before or after the serial number , above it or below it .
Frame numbers usually went on before painting and got their serial number as they were made .
The final serial number got stamped into the crankcase by the despatch department.
A lot of mistakes were made as you can imagine and the despatch books have a lot of cross out, renumbering and numbers out of sequence .
Silly things like a bike failing the final inspection could be sent back for repair then go out with the next order.
Bikes were built in batches and where possible against orders .
The competition shop stamped their own numbers which of course would be out of sequence with the main assembly lines and the same often happened with special orders so for WM20's as an example engine numbers got stamped into crankcase to match the frame number which was difficult to change