Kaolin is an aluminium silicate clay mineral also called China Clay. Talc, also called "talcum powder" is a magnesium silicate mineral. For soap manufacturing Talc and Kaolin are sold in white powder.
Kaolin and Talc are inert materials, which means they take no part in chemical reactions. they are also both insoluble in water, so they do not dissolve.
The talc is much whiter than kaolin; while this last is much easier to disperse into water than talc, which tends to sit on top of the water.
Kaolin is more used laundry soap bars, since usually it is cheaper than talc, while for white toilet soap, where whiteness is required, the best chose is talc.
Kaolin gives the structure to the soap, but the most important function of kaolin is to reduce cost of the final soap bars