We generally refer to the higher grits (1k and up) as polishing grits because the actual edge width doesn't get significantly finer after that.
I've recently been thinking that this kind of notion can be taken as far down the scale as 300 or 400 grit. I can get an edge to cut hair at those grits and if the edge is thin enough to grab hair, it can't possibly get
that much thinner, so everything from there on up is polishing the edge into a smooth, even, bevel that can be used for a comfortable shave.
The higher grit stones are definitely removing metal, but the term sharpening looses it's meaning once the edge meets at that single line, from then on you are honing, or polishing, out the irregularities.
Correction: the Verhoeven sharpening experiments document shows an improvement from about 3 microns edge width at 200 grit (from one high ridge to another, not accounting for the valleys that are closer together) to 1 um EW at 1000 grit, to 0.5 um EW at 8000 grit, to 0.35-0.4 um EW after stropping with CrO pasted leather strop. So an increase in sharpness of at most 3 microns can be expected after the initial bevel is set. To me, an improvement of 0.003 mm isn't sharpening, per se, but then this is just a difference in terminology.