SparkyFX:
The burr that is left will vary in size. It can be large enough to see with naked eyes. It can be so fine that it's more practical to feel it.
I figure HSS starts smearing the hotter it gets, which you avoid in a manual process by dipping it in water.
That's a nice-sounding theory. There is no website or YT video from which you will learn exactly why the burr forms. So the following explanation if from my own personal experience. Feel free to not believe it.
beyond this line, you won't find much corroboration; this is years of my own observation and experience. So I state it like fact, but I might be misinterpreting cause/effect. It's just more convenient to state it like fact than to hedge every sentence.
***********************************************************
The burr formation has nothing to do with coolant or temperature. It is related to the amount of burnishing. What's burnishing? If there's enough pressure, the abrasive cuts. Under that, this thing called burnishing occurs. And it's never 100% cutting and 0% burnishing. There is some mix of each occurring whenever you use almost any abrasive. If the material is cut, the abrasive scratches a chunk of the material away. Where it gets burnished, the skin of the metal is moved but no material is removed. I believe the burr is at least partiallly related to burnishing, because in my experience, the more you make conditions favorable for burnishing, the faster the burr grows. Dull/glazed grinding stone/wheel increases the rate of burr formation. Larger contact area increases rate of burr formation; i.e., if you are grinding an edge using a flat stone, you will find the blade with a wide flat bevel is going to form burr faster than the one with a very thin bevel (this is a benefit of putting a small secondary bevel on an edge on a tool like a chisel. The edge can be honed faster and without creating as much burr.)
Notice I said "rate." How big the burr eventually gets also kinda depends on how much you had to grind and how rough the edge is. If you started with a burr free edge and only grind it a tiny bit, the burr won't grow very big. But if you grind back a lot, that burr will grow longer, but it might fall off by itself in chunks as it gets too long. So it may be limited. Generally the finer the edge, the smaller the burr will be. With a coarse stone, you can make burr that is huge and looks like a string of confetti.
Anytime you grind a new edge on any steel, you should expect to have left a burr there. (Maybe most other metals, too). It happen on a power grinder. It happens when grinding or filing by hand, coolant or no. Exception is with some abrasives, like a crumbly stone that gets a lot of lapping action and surface wear/unevenness, the burr might just about erase itself as it goes... but the edge might also be getting slightly rounded more than it need be. I have a stone that is difficult to make any burr, but it also doesn't make a sharp edge.
IME lapping tends to leave less burr than filing. I think the particles tend to round over the very edge, just slightly. When routing a groove on say a router table using an endmill, the leading and traling edges of the stock tend to cut very slightly deeper, because of flex in the setup. When the bit is only partly on the material it doesn't deflect as much. By the time the entire face of the bit is on the material, the deflection is slightly greater, hence the cut gets slightly shallower compared to the edge. With a fine enough instrument, you can measure it; under enough magnification, you can see it. This is sometimes called "snipe," and if the groove must be exact to the end, you might just start with a longer piece and cut it down after you're done. With lapping I believe something similar happens. The particles at the edge will kinda be free to roll and pop up as they get out from under the edge of the material and wipe a bit of the burr off, I think, but also round over the edge just a hair. Stropping is a perhaps slightly more controllable way to do this, wrappign "around" the edge but using only very fine compounds to wipe away the burr and polish up the edge while making minimal change to the existing edge geometry.