When ordering parts, it is essential that your car is identified exactly, by model year and serial number. Since many part changes were made during model years, the commission number, engine number, and body number provide the only positive identification. Quite often a car's registration will not show the correct model year.
The commission number is one which should live with your car forever. Engines, gearboxes etc., can be exchanged and thus new serial numbers will appear on those major units. The commission numbers live with the body shell and chassis assemblies.
It appears that Triumph used the body number as a separate identifier, but they seem to have always used the commission number with the numbers reversed and letters used as a suffix rather than a prefix: thus a car with the commission number CC53876 would have a body number of 53876CC.
For ease of use we use model years as applications wherever possible.