Technically the same. Inter refers to the location in relationship to the compressed gasses. Aftercooler refers to the location of the device. Whats important is the type used ex. Air to Air, Air to coolant.... I read aftercooler is not commonly used anymore even though it's more tecnically correct for a vehical application, comparied to lets say an aircraft which would be better named an intercooler. Hope this helps!
Heat exchanger, Charger cooler, After cooler, Intercooler
The correct term is after cooler, but it apparently wasn’t “sexy” enough for the car manufacturers. The few who used it correctly has since changed their naming to fit with the popular conversation. So, though popular misuse and conventional logic, inter cooler has become established as the common term.
Other useless information:
Instead of relying on Air to air or dealing with a bunch of plumbing issues, many racers have opted for a closed system Charge cooler. It consists of cold box with either a reservoir of coolant that is circulated in a loop or just a box filled with ice, refrigerant sized for the expected duration of the run. It acts more like a heat dump. Since there is no way to release the heat while the vehicle is in motion.
An intercooler, or charge air cooler, is a device used on turbocharged and supercharged internal combustion engines to improve their volumetric efficiency by increasing the amount of charge in the engine and lowering charge air temperature thereby increasing power and reliability. It is also known as a charge air cooler, especially on larger engines that may easily self-destruct with high intake-air temperatures. The inter in the name refers to its location compared to the compressors; the coolers were typically installed between multiple stages of supercharging in aircraft engines. Modern automobile designs are technically aftercoolers because they appear most often at the very end of the chain, but this term is no longer used.
A charge cooler charge cooler, (heat exchanger) uses water or a water/antifreeze mix to cool the charge, then cools the water in a separate radiator. While heavier and more complex, charge coolers can often make arranging the rest of the engine much simpler. This approach is also known as Water-To- Air (WTA or A/W). A variation on this type of charge cooler substitutes a reservoir of coolant for the radiator, allowing the use of an ice water mixture or liquid nitrogen that can bring outlet temperatures well below ambient air temperature even under very high boost pressure. Because of the limitations on the volume of coolant that can be stored and circulated, this approach to charge cooling is only practical for short durations, making it most common in drag racing and land speed record attempts.
* an unreliable source for quotable, easy to find information on most subjects is Wikipedia. Below is a link to what is listed above.
I thing that terminology originally goes back to WWII where two stage supercharging in aircraft was common. Intercooling being between stages (if applicable) and aftercooling being after the second stage. Aftercooling being the most common during that time period. Of course that terminology has evolved to something different today.