A2 and C2 are similar in difficulty but C means that the gear can be removed while A means that there are fixed points of aid on the route.
That would be incorrect.
In an attempt to quickly simplify the difference between those two ratings I left out a lot.
It is my understanding that A means that it is an aid pitch. Some of the gear may be clean, but there will be hammering as well.
The C implies that the entire climb can be done clean, meaning that you won't have to hammer and all of the gear that you place can be removed.
I assume (maybe incorrectly) that with either grade you may or may not encounter permanently fixed gear.
As for the difficulty, I probably shouldn't have compared the two (and I knew someone would call me out) because I've never led a real aid pitch.
Am I mistaken in regards to anything I've just written?