I believe that sand, silt, clay are defined by size. But are they also generated by different processes and from different materials? Alternatively do sand particles ultimately weather to make silt, and do silt particles ultimately weather to make clay?
Sand to silt is a physical process, silt to clay is most often a chemical process.
Clay is a different creature entirely, for a start there is a disagreement about the definition of clay across disciplines. Several disciplines of geology use different size based definitions. Clays can for from physical or chemical processes depending on the type of clay. Most often clay form from the hydrolysis of tiny mineral particles.
Clay is a sort of fossilised silt, but differs from silt in that it has a much smaller grain size and in its water content, which gives it plastic qualities. It is formed from the weathering of rocks, and as rocks vary, so does the colour and chemical composition of clay. The particles are deposited in calm water such as a lake. Although clay has a silicate content and in part could include the weathering of sandstone rocks, it couldn't be formed entirely from silicon dioxide sand. Although the weathering of sand and sandstone make a contribution to the mix that forms clays, it can't be their sole constituent. It is conceivable that silt particles could form a mudstone and weathering could further reduce particle size so that it became a clay.
Factors Influencing the Rounding of Sand Grains, Victor Ziegler (1911) says that collisions of small sand grains in water are effectively cushioned by the viscosity of water, so that sand grains will not be made smaller than 0.75 mm. by water action. Wind action can erode them smaller because of the lower viscosity of air. (I don't know whether this theory is still accepted today.)