Porcelain like ceramics are made of kaolinite Al2Si2O5(OH)4. After baking they form aluminum silicates aluminum oxide and silica. The Chinese perfected this. Other ceramics ranging from bricks to earthenware are made from various clays, feldspars and quartz. Technically, any inorganic material made via the action of heat is a ceramic, and if mixed with a metal, it is called a cermet-used in electronics, high frequency transformers, ferrite magnets and in military armor (i.e. saturating a cake of boron carbide with molten aluminum would form a rather tough cermet armor plate as listed here
http://davidwoolsey.com/asmrb/examples/darpa_armor.html ).
Most of our white pottery ceramics contain aluminum oxide or magnesium oxide (hardness 5.5 or about that of an arkansas stone) so you could consider unglazed porcelain to be a random grit sharpening stone.
Ceramic is such a nebulous term since it applies to hundreds of different things, if not thousands. Almost all abrasives are ceramics... green chrome dioxide, aluminum oxide or ruby stones, silicon carbide, boron nitride, the titanium carbide used to coat the tips of drill bits... all are ceramics. Zirconium dioxide is often mixed with aluminum oxide for grinding wheels that stay cooler and zirconia is used in making ceramic knife blades and crock sticks. Boron nitride has two crystal structures, one resembling graphite and is used as a lubricant, the other is cubic like diamond and is used in place of diamond for grinding iron and steel alloys.
As far as sharpening stones go, ceramic seems to be a blanket term for any stone containing aluminum, zirconium or chromium oxides that don't requre soaking in oil or water... Even Shapton stones are called ceramic, though they are bonded with a plastic substance resembling epoxy.