Refrigeration is a process of producing cold or a process of taking away heat.
Whenever the temperature is to be lowered below the surrounding temperature, it has to be done through a process of cooling.
Heat always flows from a higher temperature region to a lower temperature region. If we have to lower the temperature below surrounding temperature, it requires external energy, as we would then be working against the laws of nature.
To understand this better, we can take the example of water. As we know, water flows from a higher level to a lower level, irrespective of the quantity involved. And if we want to raise water to the higher level, we require pumps which in turn require external energy.
Exactly similar is the case with heat energy. We therefore require external energy when using a refrigeration system with a compressor to pump out the heat from the place, where we do not want it to a place where it is not objectionable to discard this heat.
Air conditioning is a form of refrigeration. When we use air as a medium for cooling, we call it air conditioning.