As far as I have understood, white balance setting is due to the nature of light, as a white card is used for custom white balance setting.
exposure is what the camera decides will be the best for a given photo. So if its a white curtain on sunlight and shot is for inside, it might think the curtains could be overexposed and try to reduce the exposure level, and the camera tries to make it 18% Grey and set its exposure.
So how using a gray card is exposure fixed? like using a white card to set the white balance, how is the exposure set ?