I may be wrong and am happy to be corrected but as far as I am concerned the White and Black sliders are the same as adjusting the white and black points on the tone curve. These points are the little triangular adjustment points on the bottom-right and bottom-left on the curve. Moving these inwards (left and right) will push the whites and blacks out so that whites are whiter and black are blacker.
In the end, everything that the standard adjustment sliders do can be done in the tone curve except they make life a little easier for those who donât want to use the tone curve.