There are two different types of xenon arc lamps: xenon short-arc (which I consider to be "true" xenon), and metal halide, which is often called "xenon HID", "HID xenon" or just straight "xenon" (I guess because the word "xenon" is far more marketable than "metal halide"). While calling a metal halide lamp "xenon" isn't technically incorrect because the lamp does contain some xenon, it is
primarily a metal halide lamp so calling it metal halide is more precise and far less confusing (especially since xenon filled incandescent lamps are also referred to as "xenon"). The xenon is only used to provide light for the first few seconds during start-up, after that it does nothing and the lamp acts as just a normal metal halide lamp. A more precise name would be "xenon metal halide" which also differentiates between non-xenon metal halide lamps.
Xenon short-arc lamps are very inefficient which means that they draw a lot of power and aren't very bright, but have a very small arc and are extremely intense which allows then to throw extremely narrow laser like beams which can illuminate targets miles away with ease. They are also very expensive, with the cheapest being the Maxabeam at $1800. Other xenon short-arc lights include the Xenonics Nighthunter and Nighthunter II, the Megaray (125 and 175W versions), the "Plasma Beam" which seems to be vapourware, and the cheap Chinese Maxabeam clone the "Supernova" which is the cheapest at ~$500, but was only available in a former group buy.
Metal halide lamps are the opposite; they are extremely efficient, but have a (relatively) long arc and relatively low surface brightness which means that they put out a lot of light, but in a broad flood like beam with less (but still adequate) throw than xenon short-arcs. They are cheaper and much more common than xenon short-arc lights, and are also much more practical because they put out much more light, run longer, and are both smaller and lighter. All the lights listed so far in this thread are xenon metal halide.
The difference in efficiency between the two types is so great that a 35W xenon metal halide lamp is brighter than a 175W xenon short-arc lamp. To see how the two technologies compare look at the beam shots by Kenshiro
here. You can see that the metal halide X990 and Kumkang are by far the brightest, but also have a much wider beam than the xenon short-arc lamps and aren't to reach anywhere near as far. Rest of the site
here.