There is some confusion in terminology between aftercooler, intercooler, and charge-air cooler.
The inter prefix in the device name originates from historic compressor designs. In the past, aircraft engines were built with Charge Air Coolers that were installed between multiple stages of supercharging, thus the designation of “inter”.
Likewise, the “after” prefix refers to cooler placed at the end of supercharging chain.
While multi-stage turbocharger systems are still in use today, the terms intercooler and aftercooler are most often used synonymously, even in single stage cooling devices where a single cooler sits between the turbo and the engine. Both terms are used interchangeably.
Thus, since an intercooler or aftercooler commonly cools charged air, they are both referred to as a Charge Air Coolers.