For the technically minded re wet & dry developed by 3M

Materials used for the abrading particles are:
flint: no longer commonly used
garnet: commonly used in woodworking
emery: commonly used to abrade or polish metal
aluminium oxide: The most common in widest variety of grits, lowest unit cost; can be used on metal (i.e. body shops) or wood
silicon carbide: available in very coarse grits all the way through to microgrits, common in wet applications
alumina-zirconia: (an aluminium oxide–zirconium oxide alloy), used for machine grinding applications
Chromium(III) oxide: used in extremely fine micron grit (micrometre level) papers
ceramic aluminum oxide: used in high pressure applications, used in both coated abrasives, as well as in bonded abrasives.
Sandpaper may be "stearated" where a dry lubricant is loaded to the abrasive. Stearated papers are useful in sanding coats of finish and paint as the stearate "soap" prevents clogging and increases the useful life of the sandpaper.
The harder the grit material, the easier the sanding of surfaces like wood. The grit material for polishing granite slab must be harder than granite.