There are two quite different smoothing jobs in pottery and they use different tools. Smoothing wet or leather-hard clay is done with kidneys and sponges and makes no dust. Smoothing fired ware is done with diamond abrasives and, done dry, makes exactly the dust this hobby exists to keep out of your lungs.
Smoothing before firing
A rubber kidney over leather-hard clay removes tool marks and evens a surface without taking away material; a damp sponge softens and blends. This is where nearly all smoothing should happen, because it is quick, it gives a better finish than abrasion, and it produces nothing to breathe. Getting a surface right at leather hard removes most of the reason to sand later.
Diamond pads, discs and blocks
Diamond abrasives cut fired ceramic, which nothing softer will. Pads are flexible and follow a curve, discs fit a rotary tool, and blocks are rigid for flat edges. They are used to take the sharp edge off a fired foot ring so it does not scratch a table, and to remove a stilt mark or a small glaze run.
Wet, always
Every one of those abrasives works better wet and, used wet, produces a slurry instead of airborne dust. Dry grinding fired ceramic releases respirable crystalline silica in exactly the way the whole safety discipline of this craft exists to prevent. Water in a tray, the piece wetted, and a wipe rather than a blow to clean up is the entire method.
What not to reach for
Ordinary sandpaper on fired ware is useless and on dry greenware is a dust hazard for no benefit over a damp sponge. Angle grinders and stone-cutting discs are for masonry and are unnecessary at studio scale. Diamond hand pads do everything a hobby potter needs and are inexpensive.
Questions people ask about clay smoothing tools
How do I smooth fired pottery?
With diamond pads or blocks, used wet. Nothing softer cuts fired ceramic, and dry grinding releases silica dust.
Can I sand greenware?
Better to smooth it at leather hard with a rubber kidney or damp sponge. Dry sanding makes dust and gives a worse finish.
Do diamond pads wear out?
Yes, gradually. Used wet they last much longer than dry, as well as being far safer.