Interesting topic about polishing/burnishing !
At first, we could think it is a difference of abrasion, but I am slowly understanding that it is not that simple and depending of the type of stone you can be very surprised : a mid grit mid hard stone, freshly lapped, will abrase like hell and will surely make a kasumi easily with a normal amount of pressure. But as the surface of the stone get polished by the knife and abrasion, the stone start to glazed and will not abrase as it was and will finally only burnish : the iron was very dark will become very light color and details will appear. I really advise people who want to try jnats for their ability to show details to try a mid hard/hard mid grit stone because you can really play with the stone and get both kasumi and burnished surface really easily. Most important, those mid grits don't scratch when you start burnishing, meaning start to rub a knife on a hard closed surface with only water. What finer harder stone will most often do (but there is exception).
For the awasedo, it is different : Most hard stone (razor stones and most tool stones), will be so hard and maybe because of the abrasive size, will pull on the iron if you try to burnish with pressure and without slurry, meaning you will get a huge scratch like a comet on your bevel and stone. That's why, most users keep the slurry on those stones and use light pressure : you keep the abrasion and you don't directly rub the knife on a hard surface.
But there is exception ! and that's when you realise you know about nothing and you realise nature can make some crazy things : I got a stone that will only burnish, which is very hard, and will not pull iron at all. Like magic. Why it does, I don't know ! but there is something in the texture, the composition of the stone, even that it is so hard, that will avoid that pulling effect.
@KenjiF I am not sure about what you say : if I burnish a surface with synthetic, then my jnat will struggle to abrase. If you go directly to a very hard stone, maybe, because you will put a burnished surface on the hard (maybe burnished if you did not lapped) surface of the stone. But most of the time, after a synthetic progression, even if you get a perfectly burnished surface at the end, you will grab a soft or mid soft jnat to make the bridge and burnished or not, the stone will abrase the knife and will quickly make a kasumi.