In knifemaking, I have made an informal study of these compounds to help me in polishing and sharpening. Most of the information can be confusing and way too complicated. The following is the very condensed "Reader's Digest" version of information that I've found. So lets get to the good stuff.
Stropping Compounds are buffing compounds that are used in polishing metals and/or plastics. They are abrasives. Think of them as sandpaper with no paper.
Most compounds are made of three mineral components, which are listed below. They range from a super aggressive to very mild.
All of these mineral compounds are measured in grain size measured in 1- 12+ microns to help separate them in aggressiveness.
Think like grit in the sandpaper you use, except, the larger the number the more aggressive. In the process of breaking down, they break apart in different forms; round or crystalline. Crystalline is more aggressive in its cutting of the metal on your carving knife.
Chromium Oxide -
Green, very hard, very small round grain that produces very fine scratches. Use this for slow, fine, stropping on a handheld strop. This is a finishing stropping compound that produces a super smooth cut.
Aluminum Oxide -
White, Hard, small crystalline grain that produces a fine scratch pattern. Use this for faster cutting on your handheld strops for polishing and sharpening. This mineral is the same mineral as used in sandpaper for smoothing wood.
Silicon Carbide (Silica)
Black or grey, Hard, medium to large soft crystalline grain which produces a rougher scratch pattern for use in more sharpening than polishing. This is the same mineral used in the black sandpaper used in sanding metals and in the popular Scary Sharp Method.
Sometimes you may run across white, pink or yellow compounds. These compounds are formulas containing calcium carbonite, calcide alumina and no aluminum oxide (usually all white minerals) that without colored dies put in them would not be distinguishable from each other when laying on the bench. Some have more of one component than the other, making it more or maybe less aggressive.
All of these compounds are worthless unless you can get them to stay on your strop or honing wheel. These Compounds are then mixed with a binder such as Waxes (bee & Paraffin), petroleum based Oils, petroleum greases, tallow (beef or vegetable) and natural oils and combinations of these to produce a solid or paste type consistency. You can add wax or grease to fine tune the cutting ability of the compound. Not all buffing and stropping compounds are made of only these minerals. I've only stated the most common. Other stropping and sharpening compounds have diamond and ceramic pastes that are combined with these more common abrasives.
There are many stropping compounds that have different elements to produce different colors and cutting features. They are like everyone's chili recipes. We all have one and they all are great with characteristics that appeal to each individual.
So how do I decide what to use? Try them out. Use the compound that gives you the best edge the fastest while leaving your blade clean. Keep Carving!