To add to your confusion, Russian ships had genuine turrets derived from French designs while Japanese ships had barbettes with an armoured shield over the guns, invariably (but not strictly correctly) called a turret.
In the original barbette mountings, the guns were mounted on a turntable protected by an armoured tube. The guns fired over the top of the tube. To reload, the gun was elevated so that charge and shell could be rammed from within the shelter of the tube. Various forms of shield were gradually added to protect guns and crew, eventually taking the form of a complete gunhouse at which point they started being called turrets. The tube was also gradually extended deeper into the ship to protect the ammunition supply.
In the original turret mountings the guns were mounted in an armoured cylindrical box which rotated on some kind of bearing on deck. The guns fired through ports. In the French style turret, the structure extended as an armoured cone right to the ship's bottom where the point sat on what was called a "hydraulic pivot". The difference between the two systems became a bit blurry as they evolved but was very obvious at the start. (It's often said that the Russians abandoned the system and adopted the barbette/turret mounting but in fact if you look at plans they stuck with the French turret system right through to the quadruple 16-inch mountings they were contemplating in WW1.)
You've already found a pretty good description of the barbette, it's worth looking at the turret page as well:http://www.cityofart.net/bship/gun.html