Air conditioning is defined as a system for cooling and condensing the humidity and purity of the air circulating in a building. So this would apply mainly to workplaces and homes. Climate control has a broader meaning. It can cover any situation where the climate had to be carefully controlled for some reason: eg hydroponic growing systems, where everything needed for growth (food/light/air/heat) is controlled, packaging designed to absorb humidity and so preventing oxidisation or rusting, or filtering particles - such as pollen - from the air.

If you're talking about air conditioning and climate control in a car, air conditioning is where your car is cooled by a small refridgeration unit powered by the engine and battery. That is why you get slightly worse mpg when you run the air con. Climate control is normally found in higher-spec cars, as an alternative to the dial you use to turn from cold to hot. You can specify your desired temperature in degrees.

Aircon is simply a cooling system, it simply cools the air. Climate control uses a thermostat (like central heating), so when the temperature rises, on comes the aircon. When the temperature falls too much, on comes the heater. This way it is cheaper to run in terms of petrol used and theoretically more comfortable to passengers. In reality the idiot manufacturers stick the thermostat on the dash where it is heated up by the sun coming through the windscreen, and is about as useful as winding down your window. Anyone want to buy my second hand climate control??

Cliamate control is also defined as air dehumidifing. my car kicks in the climate control, even when the heating is on to dry the air and prevent misting of the windows