Singer machines of various models with a centennial badge have been documented from 1948 to 1953 and the actual centennial for Singer was 1951.
I'm not sure what the model changes were for the numbers after the model number. The only real change I know they made to the FW(other than decals) was moving the little tension thing for winding a bobbin from the lower front of the machine up onto the bed so the machine could sit in a table or cabinet.
The letter designations just tell you where they were manufactured, for example a 221K comes from the Scotland factory.
Cari