Jet Ski is the brand name of personal watercraft (PWC) manufactured by Kawasaki Heavy Industries, Ltd.. The name, however, has become a genericized trademark for any type of personal watercraft. Jet Ski (or JetSki, often shortened to "Ski"[1]) can also specifically refer to versions of PWCs with pivoting handlepoles known as "stand-ups".
A jet-ski and wave-runner both fall under the category of "PWC" (Personal Water Craft). There are a couple of other craft which fall under this category, such as the Innespace Dolphin (search it - I can't post links yet).