Black will usually be silicon carbide, these days. The term 'emery' often implied aluminum oxide in the past; but these days, it could be either SiC or AlOx, maybe even a blend of the two. There may also be some dark gray/blackish aluminum oxide compounds that look similar. But I think SiC is generally prevalent and more popular for the black. Black is very aggressive in metal removal for a wide range of steels.
True 'red rouge' is iron (ferric) oxide. Color of those is true to the name, essentially blood-red (incidentally, iron oxide is what gives blood it's red color). Not to be confused with some pink/maroon compounds, which would likely be aluminum oxide (sometimes called 'ruby').
The differences in how they work is more about hardness of each type, and less about grit size. Iron oxide is the least hard and it won't cut metals very aggresssively, no matter the grit size. It's generally intended for use on softer metals used in jewelry-making, like gold, silver, etc. Chromium oxide is probably twice as hard as iron oxide, but still considerably less-hard than aluminum oxide compounds and SiC, diamond, etc. Green works best with simple carbon and low-alloy stainless like 420HC; it will polish these steels easily, but will begin to struggle with more wear-resistant steels (440C and beyond).
For steels like D2 or 154CM, aluminum oxide compounds work well for polishing in general. BUT, with D2 in particular, a diamond or cbn compound will do a much better job cutting, shaping and refining D2's very large chromium carbides at the cutting edge, especially if the compound is used on a very firm substrate, like wood. I wouldn't use anything less than aluminum oxide on D2, for any purpose.
White bar compounds are usually aluminum oxide. Make sure they're labelled for use on hard metals or stainless steel. They will be very good polishers and edge-refiners on mainstream stainless steels like 420HC, 440A/C, 154CM, VG-10, etc. As mentioned above, they'll polish D2 pretty well, but the large carbides in that steel will respond better to diamond/cbn, especially at a more polished finish.
