IMO Gauge is the correct term if connected with 4, 8, 10, 12, 20, or 28. Gauge is arrived at by calculation not direct measurement. Shotgun gauge is the quantity of lead balls of bore diameter in a pound. Wire and sheet-metal Gauge is similar, the smaller the item, the larger the gauge.

The measurement of old cannon size in pounds was common; a 6 pounder, 16 pounder, etc (based on the weight of the lead ball). I don't know if the term 6 Pound Bore was used, if it was then I'll stand corrected on whether bore or gauge is the more accurate term.