For what it’s worth, https://en.wikipedia.org/wiki/Evaporative_cooler takes the perspective (in one paragraph) that “Vapor-compression refrigeration uses evaporative cooling, but the evaporated vapor is within a sealed system, and is then compressed ready to evaporate again, using energy to do so.” So, in this perspective, evaporative cooling is a part of the system and forced recirculation (requiring the energy source mentioned in the question) is another.
heat pumps not refrigerators
Note that what is colloquially called a heat pump is the same fundamental thing as a refrigerator — equipment is referred to as a “heat pump” when it is used for heating rather than, or in addition to, cooling, but the processes and principles are the same (with the addition of a “reversing valve” so that the direction of operation may be changed, when both heating and cooling are wanted).
For what it’s worth, https://en.wikipedia.org/wiki/Evaporative_cooler takes the perspective (in one paragraph) that “Vapor-compression refrigeration uses evaporative cooling, but the evaporated vapor is within a sealed system, and is then compressed ready to evaporate again, using energy to do so.” So, in this perspective, evaporative cooling is a part of the system and forced recirculation (requiring the energy source mentioned in the question) is another.
Note that what is colloquially called a heat pump is the same fundamental thing as a refrigerator — equipment is referred to as a “heat pump” when it is used for heating rather than, or in addition to, cooling, but the processes and principles are the same (with the addition of a “reversing valve” so that the direction of operation may be changed, when both heating and cooling are wanted).