Yes, Evaporative Coolers are the same as Evaporative Air Conditioners. The words can be used interchangeably, however have the same meaning with regards to types of Air Conditioning.

The following words also have the same meaning; Evaporative Coolers, Evaporative Air Coolers, Evaporative Air Cooler, Evaporative Cooler, Evaporative Cooling, Evaporative Air Conditioners, Ducted Evaporative Cooling and Evaporative Air Conditioning.