There is a point at which the camera’s sensor cannot pick up or record useful data. Black level is the lower bound set by the manufacturer and subsequently the user to clip it. However, it is not a denoise tool and can cause an undesirable colour shift.
Exposure is basically the doubling and halving of linear intensity. It is the easiest to understand because it coincides with camera adjustments of shutter speed, aperture, ISO and metering.
Brightness is more abstract because there are multiple definitions, implementations and applications of it. In contrast to exposure, it is less mathematical and more empirical, relating to the perception of light by our eyes, brain, and depending on the subject and surroundings.