It was also possible that DMV office personnel in the same state used the Vehicle Serial Number at some times and the Engine Serial Number at other times.

I found both codes used on different Titles/Registrations from two states (in the same year): VA and WA

old sarge,

What is your Engine Serial Number? stamped into the block behind the distributor?

What is your Vehicle Serial Number? stamped into the ID plate on the cab - between the driver's side hinges?

1951 Chevrolet Trucks serial number locations (and coding).

If both your codes are for 1951, you have "numbers matching".

Other codes that are useful for IDing an engine (people can change the Engine Serial Number), are casting codes and date casting codes for head/block.
here are locations of various engine codes