I think this was something that developed as 3E was being designed. If you read the 3.0 books in order cover to cover you find that in the PH Charisma is basically what we've always thought it is (being a pretty pretty half-orc), and oddly enables spells for bards and sorcerers (and turn undead, and paladin abilities).
The DMG brings up ability damage. Wisdom damage hurts your ability to not be influenced by others, while Charisma damage hurts your ability to influence others.
The MM brings up non-abilities. A creature with no Wisdom can not perceive the outside world and has no will-power over itself. A creature with no Cha can not perceive the difference between itself and the outside world (no self-awareness) and has no will-power over others.
Thus Wisdom determines your ability to resist the will of others and your perception of the world (spot, listen). Charisma determines your ability to assert your will onto others and your self perception.
So a cleric becomes more aware of his god and more able to control the divine power granted to him with more Wisdom. A druid becomes more in tune with nature and able to channel it's awesome might.
A sorcerer or bard becomes more aware of their own latent power with Charisma, and becomes better able to harness it to affect the outside world.