You are correct that evaporation of liquid occurs when heat is added to the liquid. This heating can come from either the gas phase (in the form of convection) or from heating the liquid (in the form of conduction). But the term, evaporative cooling refers to the cooling effect produced due to the evaporation of liquid. To give a very simple example - why does your body feel cooler when you sweat? Evaporation occurs at the surface when the liquid molecules near the surface experience collisions. These collisions increase their energy. When this energy is above the surface binding energy, the liquid molecules ar the surface evaporates. The energy required for a sustained evaporation comes from the internal energy of the liquid, and hence the liquid experiences a temperature reduction, or simply put - a cooling effect. For a sustained evaporation, the energy lost as latent heat by the liquid needs to be provided by an external means (such as conduction, convection, or radiation). I hope this clarifies the concept. Thanks.
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