Well, technically, CAT II and CAT III refer to approaches, not landings per se. And their main difference between a CAT I ILS approach is the weather minimums for that approach.
Here's the breakdown out of the "Chart Glossary" Section of the Jeppesen Airway Manual...
ILS CAT I - Hieght above Touchdown (HAT) of no less than 200 feet, Runway Visual Range (RVR) not less than 1800 feet.
So, in that case, the cieling can be no lower than 200 feet above the Touchdown Zone Elevation (TDZE - Highest portion of usable runway in first 3000' feet of runway surface), and visability can be no less 1800 feet RVR, which equals about 1/3 of a statute mile.
ILS CAT II - HAT no less than 100 feet, RVR not less than 1200 feet (1/4 of a mile)
ILS CAT IIIA - RVR no less than 700 feet
ILS CAT IIIB - RVR no less than 150 feet
ILS CAT IIIC - No RVR requirement
Notice there are no Decision Altitude requirements for CAT III approaches....
The CAT III approaches contain the note, "Special authorization required." This relates to certification of the aircrew, and the aircraft for that type of approach.
Anyway, that's all I know about it. If anyone else has more info, feel free to share.
Jack @ AUS