The supporting role of backings and bonds
The backing's stiffness and flatness influence the quality and speed of the sandpaper's cut. For the most part, manufacturers choose adhesives and backings to augment the characteristics of a particular abrasive grit. You will have a hard time finding an aggressive abrasive mineral, for example, on a backing suited to a smooth cut.
The stiffer the paper, the less the abrasive minerals will deflect while cutting. They will cut deeper and, consequently, faster. Soft backings and bonds will allow the abrasives to deflect more, giving light scratches and a smooth finish. You must even consider what's behind the backing. Wrapping the sandpaper around a block of wood will allow a faster cut than sanding with the paper against the palm of your hand. For instance, an easy way to speed up your orbital sander is by exchanging the soft pad for a stiff one (photo below). The other consideration is the flatness of the backing, which has nothing to do with its stiffness. Flat backings position the minerals on a more even level so they cut at a more consistent depth, resulting in fewer stray scratches and a smoother surface.
Cloth is the stiffest but least-flat backing. It will produce the coarsest and fastest cut. Cloth comes in two grades, a heavy X and a light J. Paper is not as stiff as cloth but it's flatter. It comes in grades A, C, D, E and F (lightest to heaviest). A-weight paper that has been waterproofed is approximately equivalent to a B-weight paper, if one existed. Polyester films, including Mylar, look and feel like plastic. They are extremely flat and pretty stiff. They will give the most consistently even cut and at a faster rate than paper.
The backings for hand sheets and belts are designed to flex around curves without breaking. This is not true for sanding discs for random-orbit sanders. They are designed to remain perfectly flat, and if used like a hand sheet, the adhesive will crack off in large sections (photo below). This is called knife-edging because the mineral and adhesive, separated from the backing, form knife-like edges that dig into and mark the work.
Adhesive bonds on modern sandpaper are almost exclusively urea- or phenolic-formaldehyde resins. Both are heat-resistant, waterproof and stiff. Hide glue is sometimes used in conjunction with a resin on paper sheets. It is not waterproof or heat-resistant, but hide glue is cheap and very flexible.
Aluminum oxide is a sharp and blocky mineral. It is the most common, all-purpose woodworking abrasive, and for good reason. It is the only abrasive mineral that fragments under the heat and pressure generated by sanding wood. This characteristic is called friability and is highly desirable. As you sand, aluminum oxide renews its cutting edges constantly, staying sharp and cutting much longer than other minerals.
Aluminum oxide is also a relatively tough abrasive, which means that its edges won't dull much before they fragment. Its friability and toughness make aluminum oxide the longest lasting and the most economical mineral.
All aluminum oxides are not created equal. 3M alone manufactures 26 different kinds, ranging greatly in toughness and friability. The toughest grades are nearly white in their raw form and are used on premium-grade sandpapers. The softest grades are dark brown and more appropriate for sandblasting than sanding. Some cheap sandpapers have blast-grade aluminum oxide on them. No manufacturer is going to tell you which kind is on which sandpaper, however, and it's impossible to judge by the color of the sandpaper because a size coat covers and colors the mineral. If one brand's aluminum-oxide paper doesn't work well, don't judge all aluminum oxides by it. Simply try another.
Silicon carbide is black and iridescent, and the grains are shard-shaped (photo below). Unlike aluminum oxide, there is only one kind of silicon carbide. It is harder and sharper than most aluminum oxides, making it the better choice for cutting hard materials, such as finishes, paint, plastic and metal. Consequently, you'll probably find the widest range of silicon carbide sandpapers in a good auto-body supply store.
Silicon carbide sandpapers for woodworking are almost always on waterproof paper and intended for sanding finishes. Though silicon carbide is a friable mineral, it is so hard that sanding wood will not cause it to fragment and renew its cutting edges. Though it will sand faster at first, it will dull more quickly than aluminum oxide. It is also generally more expensive than aluminum oxide.