There's a HUGE variety of 'white' compounds out there. Many are aluminum oxide, which itself can come in another HUGE array of grit sizes. Aluminum oxide can also be grey, pink or blue, and maybe other colors. Other 'white' compounds might be completely different stuff, like tin oxide (very soft; made for jewelry and other soft metals). One version of tin oxide is actually referred to as 'white diamond' (confusing enough?). The 'black' compounds will either be silicon carbide or something like emery (a.k.a. 'corundum', which is a naturally-occurring aluminum oxide). And 'corundum' shouldn't be confused with 'carborundum', which is a trade name for synthetically-produced silicon carbide (named 'carborundum' by the original discoverer/inventor). As with the aluminum oxide, silicon carbide 'black' compounds are also available in a very wide array of sizes.
'Green' is almost always chromium oxide (Cr[sub]2[/sub]O[sub]3[/sub]), which is usually pretty fine grit (~1 micron or smaller), down to 'average particle size' of ~0.5 micron, from decent & reputable brands. Some cheaper 'green' compounds might also be a mix of Cr[sub]2[/sub]O[sub]3[/sub] and other compounds, like aluminum oxide, each of varying grit sizes.
It's quite possible that one abrasive of relatively large(ish) particle size might be used for a 'finer' finish than a smaller grit of different abrasive. This is due to the differences in hardness or particle shape, which greatly influence how aggressive they are. Compare diamond to aluminum oxide, for example; diamond will be much more aggressive, in a much smaller particle size.
Clear as mud, right?
The best bet, when attempting to figure out a proper sequence of use, is to buy compounds of which the abrasive type (diamond, silicon carbide, aluminum oxide) and particle size in microns are clearly known ('grit' or 'mesh' numbers are often as ambiguous as the color descriptors). If they're not labelled accordingly, ask the vendor. And if the vendor can't/won't say what they are, I'd avoid them. OR, at the very least, spend some time experimenting with what you buy, to figure out how each is going to perform.
David