SUV = Sport Utility Vehicle; ok - that works. But is usually based on a truck-chassis. For example the Tahoe & Silverado, or Ram and Durango.
CUV = Compact Utility Vehicle. Its small, but is a utility vehicle (can carry relatively large amounts of crap, or people); can be based on a smaller chasis, sometimes a car, sometimes a designated chasis, like Caliber, Compass, Patriot. The Patriot is unique in that it has all the utility of an SUV in a smaller package for those of us who don't need something with a v8, and like the maneuverability that the small size gives us, not to mention classic Jeep off-road ability. Ours is not based on any car available on the market, which keeps it from being either a Hatchback or Wagon. This is why the CUV fits the bill in the case of the Caliber, Compass and Patriot.
Crossover = mix between car & suv/van; Crossovers tend to be more like the Pacifica and Mazda 5 in nature, and are closer to the wagon in size, but MiniVan in proportion. This is more for the people who don't wan to be labeled with the "MiniVan" stigma, but want to have the same functionality of a MiniVan. These are imo, basically minivans with forward opening rear doors, instead of sliding doors. [with exception to the mazda5]
Car = small people mover, can be 4 or 2 door & has a trunk for cargo, usually with flip down seats if necessary, but its purpose is carying people not things. Usually hatchbacks are derived from these vehicles, in 3 or 5 door form.
Wagon = people mover that has SOME utility, but is VERY based on a car-chasis. Magnum Wagon, Mitsubishi Lancer/Evo wagon, BMW 3&5 series & Mercedes C and S-Class wagons. Its basically a compact version of a mini van that is less people-mover and more stuff-mover. An option for those who want a car, but want to be able to carry more stuff than their car-counterpart can. These are usually extended-bodies of their given car-type however, so they wouldn't be given 'hatchback' terminology and are always 5-door in form.
Hatchback = small people mover, usually only seats 5 at most. Honda Fit, Yaris, Focus, anything really labeled as a "3 or 5 door" is usually a hatch-back, and has a sedan/coupe version of the same vehicle.
Truck = usually implies having an open-air bed from the factory; and is not really built to be a people-mover (except in some cases, like Avalanche/Escalade and "MegaCab" Rams), is built more for the function of carrying objects that don't need to be sheltered during a trip.