Compounds come in a bewildering array of abrasives and binders, but basically they all break down to an abrasive suspended in a binder or vehicle that can be applied to a substrate of some sort. In the case of diamonds that might only be water. Most use some form of stearate - veg or animal based industrial tallow.
While this is a generalization, most fall into this range:
Black - Aluminum oxide - 20-30 micron
Yellow - " - 3 micron
White - " - .5-1 micron
Green - Chromium Oxide - .5 micron
Red uses ferrous oxide and really is not intended for hardened steel. Used on a strop it might increase the burnishing effect but steel removal will be light or non-existent.
Diamond or Cbn I do not believe have any standardized color scheme and many appear to use no color binder/vehicle anyway - read the label!
Add to the above, many compounds used for woodwork/general purpose seem to intentionally favor multiple grit sizes. Flexcut Gold uses a range of 4 micron down to .5. The green compound sold by Lee Valley under their name uses a similar distribution. I likewise make use of this principle in the compound included with my Washboard sharpening blocks. Notable difference is I use silicon carbide for the abrasive and the binder is tweaked to adhere better to paper instead of leather.
The major differences that I have seen from one material to the other are often the formulation of the binder, and not the distribution or type of abrasive. Most of the ones I have looked at under high magnification maintain very tight particle size grouping and very similar from one brand to another. The binders are all formulated differently though, and play a big role in how effective a given compound might be for a given use. The backing will also play a huge role, the exact same compound can produce a variety of finishes/edge effects based on how hard or soft the backing is, how much mobility the abrasive has, and how much force is applied.
Most makers use Aluminum Oxide and this will work well right up to the higher Vanadium content steels, at which point diamond or CbN will be needed either in a compound or on a lapping film.
