I voted "
Ceramic".
"
Ceramic" instead of "
Clay" because a "clay" cup would be pretty difficult to use. If you filled it wil a water-based liquid...... the clay would absorb the water and slake down back into a plastic state and deform, eventually making a total mess all over the table

.
Seriously...... "
Clay" becomes "
Ceramic" when heated up to above about 1000 F. This happens when the chemically combined H
2O in the clay crystals is driven off by the heat treatment. Once that happens, it will not slake down in water and become "plastic" again.
In colloquial usage,
clay (as in "made of clay") and
ceramic would seem to be kinda' redundant. And as I mentioned one other time somewhere here, "
Porcelain" as a material is just a sub-grouping of a clay as a ceramic forming material. Porcelain is a "clay".
Ok...OK... too much information.
best,
............john