By the mid 1800's many makers and shooters thought a bore needed to be tight in the middle of the barrel, then relieved towards the muzzle and towards the breech. How tight they were, depended on whether ball was also desired to be shot, with less constriction in barrels for both shot and ball. The constriction also depended on the barrel's overall length.
By the 1820's, the US military found that the thicker the barrels, the more accurately they would shoot round balls, thus by 1842, the barrel was quite heavy on the issue Musket, the last of the smoothbores.
Today, the 20 bores, or .62 cal smoothbored barrels can be purchased both ways, either thick walled or thin depending on the maker.