When grinding thins the steel near the apex enough that the edge loses its lateral strength, that too-thin steel at the edge will deflect or bend away from the stone. That's the burr. It's the indicator the edge is as thin as it can usefully be, once it becomes too weak to hold up to lateral pressure.
The burrs formed in different steels of different hardnesses will behave differently when that happens. Steels at higher hardness will usually exhibit burrs that break away more easily, because the higher hardness usually makes the steel more brittle than ductile. Steels at lower hardness tend to be more ductile than brittle - meaning their burrs will bend back & forth a lot more and cling tenaciously to the apex without breaking away. They're more tedious to remove because of that behavior.
Regarding the burr being clipped off in edge-leading sharpening:
Once the burr becomes thin enough, instead of being pulled under the apex in an edge-leading stroke, the burr will bend or curl away from the stone. It'll do the same thing with an edge-trailing stroke too. It's simply because of the lateral pressure exerted against the apex on the stone, which deflects the weak burr away from the surface of the stone. Once it's deflected away, the burr can't be caught and pinched underneath the apex in an edge-leading pass from the same side. This is why it's necessary to turn the blade over, which turns the folded burr downward into the stone before taking the next edge-leading pass. Sometimes it'll be necessary to raise the angle a little bit so the burr will be folded back underneath the edge, to clip it off. But if the burr is already sharply folded to one side, it won't always be necessary to raise the angle to clip it away. You need to just observe how each burr behaves in each circumstance, and adjust your approach to handle it. It won't always be the same in how the burr behaves and therefore in the method used to remove it.
The photos below are of a burr (or 'wire edge' or 'foil edge') I created on a Victorinox paring knife's edge with some heavy grinding against a medium Spyderco bench stone lubricated with mineral oil. The photos exhibit how weak and fragile the steel becomes when thinned past a certain threshold. It literally looks like bent & crumpled foil, viewed close up. The steel used in that blade is considered to be pretty ductile as I described above - it's a low-alloy stainless at around 56 HRC, which is Victorinox's spec for that steel.
