Yes the older tractors like yours the SN on the engine was the same as the tractor but if an engine was installed from another tractor then it would be different.Later D6 tractors the engine had one number and the tractor another. Take say one model of a D6C the engine was a 3N 3306 engine SN and the tractor was 10K SN starting in 1967.
now if i want parts for the engine i should use engine #and not the machine #on back of machine thanks