Semi-submersible Drilling Rig
This type of rig is more like a ship than a Jack-up. It's main design principle is built along the lines of a ship. A drilling package is basically built on top of a barge consisting of 6-8 cylindrical legs, with pontoons at the base to aid in the moving of the rig.

Ballast tanks are incorporated into the base of the legs and pontoons and are filled with water to 'semi-submerge' the platform to provide stability during drilling operations. In addition to this, Dynamic Positioning or maybe up to 8 anchors would be used to ensure the position of the rig does not alter during drilling operations. When the rig needs to be moved, the anchors are heaved in and the ballast tanks are emptied of water which raised the rig out of the water so that almost the whole rig can be seen.

Tug boats or supply vessels are usually attached to move the rig to it's next location, though some of the bigger semi-submersible drilling rigs can move under their own steam with the aid of thrusters and GPS. Once on it's new location, the ballast tanks would be filled with water to 'semi-submerge' the rig into the sea, and the DP would be engaged or anchors set to ensure the rig does not move off location.

An oil company, ExxonMobil, Shell, BP etc would hire a drilling rig like this to drill exploratory wells in deeper water to find oil or gas before constructing a production platform on the site after confirming the existence of commercially viable resources.