An intercooler (IC) is a device which looks like a radiator, but contains the intake air. The ambient air is cooling the intake air.

A charge-cooler (CC) is a device where the ambient air cools water, which in turn cools the intake air. In essence a charge-cooler consisting of two "radiators".

WHAT'S SO GOOD ABOUT THEM?
The "plumbing" is the deciding factor. It is sometimes impossible to get big (50-75mm) air ducts from the engine to the front of the engine bay, but a flexible water pipe can be fitted easily. Another advantage of a charge-cooler is it thermal mass, which is very high due to the water. This means that the intake air will not change drastically when the car stops moving.

WHAT'S SO BAD ABOUT THEM?
Charge-coolers are less efficient and more costly than inter-coolers, because the heat has to travel over more transfer surfaces. An inter-cooler transfer is: ambient air/metal/intake air, where a charge-cooler is: ambient air/metal/water/metal/intake air. It is a thermodynamics law, which states that heat (energy) can flow only when there is a temperature difference.

GENERAL
All modern fuel injection systems, including ours, compensate for air temperature. However, cooler (denser!) air gives more power, and this is what it's all about.