I think the rule dates back to the time before cannon bores and cannon balls were made accurately. This was quite late into the mid 19th century.
Given that both bore and ball vary it would pay to match shot to the diameter of each gun on a ship or in a battery. Shot should be rather smaller than the bore of the gun, but loose balls won't shoot straight.
I think the 'Gun Diameter' scale is used to measure the gun bore. The 'Shot Diameter' scale uses the same graduations, but they are closer together. So you can sit down with a pile of shot and use the Shot scale to sort them to suit a particular gun: too big; too small; and close enough.
Might be collectable!
Dave
Late thought: bore diameter may be graduated in pounds rather than inches. Could test the idea by calculating the diameter of a 1lb cast-iron sphere to see if it matches your scale.
Edited By SillyOldDuffer on 24/11/2017 11:45:19