At some point in time ( certainly by mid 16th c. ), octagon barrels became common styling for rifles. By the 18th. c it was pretty standard, so that most German jaeger rifles, English rifles and American Kentucky rifles of that period had octagon barrels. Of course, it was not much more than styling ( maybe it's a trifle easier to adjust the sights) . And it was not a hard and fast rule: some rifles would be made to look like fowlers ( shotguns) with round barrels, some smoothbore guns were made with octagon barrels, and many rifles would later be bored out into smoothbores, when the rifling became worn. And the military would have no trouble dropping the style ( perhaps because it's more complex to mount a bayonet on an octagon barrel), with the 1814 Common Rifle and the 1803 Harper's Ferry Rifle having barrels only octagon at the breech, and the English Baker Rifle having a fully round barrel. But while plenty of rifles since 1850 or so have round barrels, any gun since then with an octagon barrel is pretty certainly a rifle.