To the best of my knowledge, the only difference between the three settings is the fog of war. You can see all the changes on the options screen. They are in the manual as well, but some of that may be out of date. Enemy units do not get stronger, and currently the AI does not do anything different.
The original names for the difficulties were Aspirant, General, Commander-in-Chief. The French word translated as Aspirant was Conscrit. Conscript might be better than Aspirant. I've requested going with Conscript, General, Grognard because people have gotten used to calling the hardest difficulty Grognard.
It really doesn't matter what we call the difficulty levels, there will still be players who think, "Hey, I never play on anything but the hardest level."
Hook