Close. As my first instructor said many years ago, there's no such thing as cold, only the absence of heat. The evaporator gets it's name from what happens to the refrigerant inside, just like the condenser. If they called it a boiler, folks would get confused.
Hot air, from the return or outside, ( depending on the box duct ) transfers it's heat to the refrigerant in the evaporator in the heater/ac box ( which boils at a lower pressure, aka, evaporates from a low pressure liquid ). This low pressure vapor, containing heat, goes through the suction line to the compressor, which raised the pressure ( and temperature, and also adds it's own heat of compression ) so that the heat can be rejected, or transferred to the medium you have available, namely the front of the car on a summer day. In the condenser, the hot high pressure vapor is condensed, ideally back to a liquid. This high pressure, medium temp liquid then goes through an orifice/valve/capillary tube/TXV/EEV/float box valve ( some kind of pressure restriction, depending on weather it's a 'fridge, window shaker, Dodge Dart, or 1500 ton chiller ) where the pressure and temperature drops, and the much cooler liquid fills the evaporator ( but not completely, or you'd have flood-back ) then the cycle continues. The vapor compression cycle folks.
