They are all charge air coolers (this is the term most often used by OEM heat exchange manufacturers and the car makers when refering to intercoolers), whether air/air or air/water. In theory water cooled CACs should be more efficient because the thermal coefficient of each fluid is vastly different (don't ask me figures!), so it's easier for water to take heat from the charge air. Air/air coolers are less efficient because even though there is a temp difference between the charge air and cooling air the thermal coefficient is the same. But all this ultimately depends on the design of the core, whether air or water cooled. Water/air CACs are not often used in mass market cars due to cost, packaging, the need for additional plumbing and the cooling water will often need it's own rad. Both normal engine coolant (with auxilliary rad) or stand alone (with seperate rad) supplies can be used.
Water spray kits will certainly help get your charge air colder, it increases the heat exchange in the same as why a wet hand feels colder than a dry hand or why your body sweats to keep you cool, the heat is more effectively removed from the surface.
