I'm not a mineralogist, but I can try to add a bit to what others have said, based on what I have quickly been able to read up.😉
Clays are made up of tiny crystals of "clay minerals" and water. The water is hydrogen-bonded to the surface of the crystals, which means it is attached by bonds that are about a tenth the strength of a full "normal" chemical bond. A crystal of dry clay mineral will tend to absorb water until there is a hydrogen bonded film of water all along its surface.
Clay minerals are made of sandwiches of sheets of silicate tetrahedra, which have a -ve charge, with metal ions in between that have a +ve charge, thus making the whole sandwich electrically neutral, and then water molecules in between one sandwich and the next. (Though some are Danish open sandwiches with only one layer of silicate "bread" under the metal ions and nothing on the top.) Because they have a sheet structure, these minerals easily cleave along the lines of the sheets, as mica does. What you end up with is a lot of microscopic, flat, very thin flakes of clay mineral, with water in between. It is the water that makes clay plastic, enabling you to mould it, as it allows the flat flakes to slide past one another. In terms of chemical bonding, you have covalent bonding within and between the silicate tetrahedra, ionic bonding between the sheets of tetrahedra and the metal ions in the sandwich, and finally hydrogen bonding of water molecules along the outside of the sheets. So clays are chemically quite complicated things, dull though they may look from the outside.
So when you ask if clay is uniform or homogenous, it depends on at what level you mean. Macroscopically it is, but at the molecular level it is made of two distinct phases, a solid mineral and liquid water - albeit much of the water is hydrogen bonded to the mineral so that it does not behave entirely like a liquid. Moulding the clay does nothing to this structure. However, drying or firing the clay will drive off most of the water, shrinking the clay and hardening it by allowing the layers to link together directly instead of being kept apart by a layer of water.
Here's a diagram I found which may help visualise it: