well, laser cutting entails using a laser that is beamed through a gas like CO2, and directed by reflective mirrors into the material being cut. It has a HUGE output in terms of Kilowatts and it very precise. The material should NEVER be reflective, though. You can use laser to cut through wood, plastics, etc.
Water Jet cutting uses a jet of water instead of laser. LITERALLY a jet of water. It is forced through a nozzle that is restrictive and causes it to come out with such a force that it erodes everything it comes in contact with. It can be used to cut through virtually any material, including metal. Its wattage is quite low, though.