In reality, nothing as it has to do with our application. In the compression business, intercooling is cooling of the process air or gas between stages of compression. Aftercooling is cooling of the process air or gas after the final stage of compression.
Intercooling is used in a lot of automotive/truck terminology because the air is indeed compressed again after it is cooled - by the piston on the engine's compression stroke. Caterpillar, however, refers to many of its gas engines as being of the TA configuration - turbocharged and aftercooled.
If you accept Cat's terminology, a twin turbo series setup with a cooler after each turbo would be intercooled after the low pressure turbo but aftercooled after the high pressure turbo.
In the case of the Detroit Diesel, a cooler located after the turbocharger(s) would be an intercooler, while a cooler after the blower would be an aftercooler.
Rusty