Potters kiln and clay kiln are buyers' phrases for the same equipment a supplier lists simply as a kiln. What differs between machines is size, supply and control, and those three between them determine what work a kiln can actually do rather than what it is called.
Test kilns and studio kilns
A test kiln is a few litres, plugs into a socket and exists to fire test tiles, small jewellery and glaze trials. A studio kiln fires a batch of work in one go and needs its own electrical supply. The mistake people make is buying a test kiln as a first kiln and discovering it will not fire a dinner plate; the opposite mistake is buying a large kiln and firing it half empty, which wastes electricity.
Controllers, and what they buy you
A modern controller runs a programmed schedule: a slow climb through the water-loss stage, a faster climb, a soak at temperature and a controlled cool. That repeatability is what makes glaze results consistent. A manual kiln fired on a dial and a pyrometer will do the same job in the hands of someone who watches it, and no kiln fires itself well while unattended.
What ages in a kiln
Elements lose power gradually and eventually cannot reach temperature in a reasonable time; thermocouples drift, reporting a temperature the kiln is not at; brickwork chips and cracks. All three are serviceable, and a kiln that is slow to reach temperature is usually telling you the elements are near the end rather than that it is broken.
Buying used
Look at the elements for sagging or breaks, the brick for structural damage rather than chips, the lid or door seal, and ask what the last firing reached and how long it took. A kiln from a maker who still supplies parts is worth substantially more than one from a maker who does not, whatever the chamber size.
Questions people ask about clay kiln
What size kiln do I need?
Large enough for your biggest piece plus shelf and props, and small enough that you can fill it. A half-empty firing costs the same as a full one.
Is a controller necessary?
It is what makes results repeatable and is standard on modern kilns. A manual kiln fired attentively with cones does the same job.
How long do kiln elements last?
They lose power gradually over many firings. A kiln that takes noticeably longer to reach temperature usually needs elements rather than repair.