Instead of discussing clays solely in terms of their chemical formulae, determined by x-ray diffraction, potters group clays into classes based on more general properties of the entire clay body, such as texture and color. One distinction potters make is between primary or residual clays, and secondary or sedimentary clays.
Kaolin is the major primary clay which is used in ceramics.
So when kaolin is fired along with some silica and feldspar, it forms a highly refractory white solid. Generally though, kaolins must be mixed with other clays to make them workable, and potters attempt to adjust them without sacrificing the relative purity of the color and the density of vitrification in the final object. Ball clays are highly plastic, and are added to clay bodies in order to increase plasticity. Ball clays are more fusible than refractive and also tend to shrink appreciably during drying and firing. I hypothesize based on the overall properties of the body that the clays are in the smectite class, allowing for a large shrink swell differential resulting in a high plasticity.