The 'stick' compounds can be almost anything, regardless of color. Problem is, many of them are blends of abrasives. Most pure 'green' (chromium oxide) compound in powder form will be ~0.5-1 micron in size. BUT, in stick form, there's no way to know for sure, what else may be blended in with the binders, or how uniform/clean the mix will be.
I have a bar of the Woodcraft green stuff. One thing I noticed, it can leave a hazy finish on polished bevels. To me, that means it's either blended with something, or there are a lot of impurities in it, at larger particle size. I've since been using some green powder form, purchased at a rockhound polishing/lapidary hobby outlet, and it seems much more consistent in the results it produces (polishes, without the haze). I mix it with mineral oil, before application to the strop.
David