Bore sizes are given in calibre ie a fraction of an inch. The "standard" for paintball is .68 . Most paint or barrels are given in 'small', 'medium' or 'large' bore, for convinience
As paint varies in size, a good match of barel to paint affects the accuracy of your shots. There are charts available on the internet such as this
one which give an indication of what you might expect.
However, as paint is affected by tempreture, humidity and storage, it's not definitive. The way to test is to put a paintball into your barrel. It shouldn't roll out, but should slide out if you blow on it. There are various barrels with inserts of different calibre such as Smartparts Freak, and ones with click adjustments such as Psycho Ballistics Aradus which make it easy to adjust for different paint.