Geologically, yes.
ClayClay is just a suspension of sandsand (tiny rocks and minerals), water, and humushumus (organic material) within extremely fine-grained igneous rocks. Technically, clay is a stone material even before you do anything with it.
Over time, heat and pressure squeezes out the water, and the humus breaks down and bonds, its minerals (such as carbon) bonding with other materials (not unlike what happens in steel-making). This is how clay becomes sedimentary stonesedimentary stone. ShaleShale is a good example of this.
FiringFiring a brickbrick within an oven ora kiln just accelerates theforces that process.
Practically, yes.
If it looks like a stone, feels like a stone, and clocks a Burning Fist guard in the head like a stone, then it might as well be a stone. Don't waste timeDon't waste time at the table pondering this sort of thing.
Rock vs Stone
Same thingSame thing, seriously, I know my players were RPing dwarves but they're the same thing. Usually rock refers to the object and stone refers to the material, but they're interchangeable, can we please enter the dungeon, please?