How Each Surface Is Built
Clay is not a solid at the top. A clay court is a layered structure, with a compacted base and drainage below, topped by a loose layer of crushed stone or brick dust that sits free above the packed material. That loose layer is the defining feature. It moves when force is applied to it, which means both the ball and the shoe interact with something that shifts rather than resists.
Grass is a living plant grown on soil, cut extremely short and rolled to compact the ground beneath it. The playing characteristics therefore depend on two variables that change during an event: the condition of the plant, which wears away in the areas of heaviest use, and the moisture and firmness of the soil beneath it. A hard court is the opposite in philosophy. Acrylic layers are applied over a rigid asphalt or concrete base, and grit suspended in those layers determines the surface texture. That means a hard court's friction is specified rather than grown, and it can be tuned by whoever builds it.