I routinely use the gray Scotchbrite (or equivalent from other manufacturers) instead of 4/0 steel wool between applications of finish t0 de-nib the surface. I find that it works just as well as steel wool but without leaving tiny bits of steel wire embedded in the finish. It's also great for applying waxes or surface treatments like Howard's Feed'n Wax.
I also keep a maroon Scotchbrite pad in a basket attached to my lathe stand for use in buffing down the bedways so that my tailstock and banjo slide more smoothly.
The white Scotchbrite pads are also occasionally useful to polish a finish without resorting to actual buffing. I've tried using both maroon and green Scotchbrite pads on wood, and they do work well, but I find that I prefer to use sandpaper. But like sandpaper, it is important to use a gentle hand with them - if you rub too hard, the color can transfer to the wood, especially if the timber is light in color.
The basket that I use is actually one of those vinyl-coated wire baskets that originally was intended to be hung from a kitchen drainer to hold silverware - it evntually collected a few cuts in the wire that led to minor rusting which my wife can't tolerate in the kitchen so it got demoted to the shop. It works great for my purposes - the fact that it is a basket means that it is a convenient place to store stuff like the Scotchbrite, a rubber sandpaper cleaner, and a pair of channel-lock pliers (helpful when a fixing gets stuck on the spindle), but shavings just fall through the wire mesh.