The downside of trying to figure out 'green', 'white', 'blue', etc., is that it depends almost entirely on the manufacturer. Green compound is recognized universally as being chromium oxide at a minimum, but there's still some variability as to the grit size & uniformity. The better stuff will be a uniform grit size (usually around 0.5 micron, give or take). And at least some manufacturers blend other abrasives into the 'green' compound. So trying to predict how they will perform is futile, without knowing exactly what's in it.
'Black' compound will almost always be silicon carbide. But it can be had in a very WIDE range of grit sizes, so it's a relative unknown, too, if only referenced by color.
'White' compound will likely be aluminum oxide (and again, at a wide range of possible grits), but there are some other 'brands' out there that are white, but utilize different abrasives. One I've heard of, called 'White Diamond', not only doesn't utilize AlOx, but there's no diamond in it, either. It uses 'Tin Oxide', a very soft rouge intended for soft metals (jewelry).
'Blue' compound, I'm guessing, is also aluminum oxide, maybe another mix of some kind. What grit, I don't know.
The best way to find out, is to ask the manufacturer or vendor where you bought it. If they can't or won't say what's in it, or what the grit size is, beware.
Here's a link to a very informative thread on the properties of most commonly-available abrasives, it's worth a read:
http://www.bladeforums.com/forums/showthread.php/776447-properties-of-abrasives-described