I want to take what marty said and clip it.
Instead of CHA being your projection of yourself on the outside world
I would say that CHA is your projection of yourself
The reason being for this is what if something were internally causing you to question yourself or take over you from the inside (example being the sorcerer without willpower points). Your charisma would represent your ability to project your clear conception of yourself and suppress that which was internally overtaking you.