The way you describe it they are literally the same thing. All the "advanced" application had to do was "not touching". That's it. You're overcomplicating it for no reason.
You can use CoA in your attack. ACoA is making it "not touching". Luffy called it "advanced".
Same thing with CoC. You can put CoC behind your attack. ACoC is making it "not touching".
"Advanced" just means non-touching. That's why Luffy could
use ACoC without 0 training.