Jet Ski is the brand name of personal watercraft (PWC) manufactured by Kawasaki Heavy Industries. The name, however, has become a genericized trademark for any type of personal watercraft. Jet Ski (or JetSki, often shortened to "Ski") can also refer to versions of PWCs with pivoting handlepoles known as "stand-ups." Sit Down PWCs are also called "Jet Skis." Also, "WaveRunners" and "Jet Skis" are essentially the same thing; but "WaveRunner" is the trademark name for Yamaha's line of water craft. Whereas "Jet Ski" is the trademark for Kawasaki's line.
Any jet ski worth driving will have a safety key. This is usually a bracelet tethered to a little plastic clip that attaches itself to a spot on the handle bars. This key needs to be engaged on the jet ski's handle bars in order for the engine to start and run. The tether should always be around your wrist; if you fall off of the jet ski and you are not wearing the tether, the jet ski will keep going. If you are wearing the tether, the plastic key will be pulled out and the engine will stop. This can be handy when it's time to swim back to the jet ski.
To right your jet ski, swim to the rear and flip the boat over in the direction indicated on the back of the jet ski. Every jet ski has a specific direction that it is easy to flip it back over and a direction that it is impossible. If you can't make it flip back over, try flipping the other way. It should be easy to right the jet ski.