The main difference is in the primer types is both by size, & by how it is designed.
Neither is strictly non-reloadable, but one is way harder than the other making it less desirable from the reloaders standpoint.
"Reloadable" ammo uses Boxer primers. they have a single big hole in the center of the case's base, this is the flash hole. Because you need to remove the old, fired primer as part of the process this is really easy to do, you just poke a rod through the hole from inside & the primer pops out as the case goes up into the die to resize.
"Non-reloadable" cases use a different system, called "Berdan". The berdan has a solid center with 2 smaller holes off to the sides. because of this you can't just poke the old one out while resizing. You need a seperate "remove the primer step", independant of the actual reloading dies. There are several systems. A claw type that pierces & levers out the old primer. A liquid type where the case is filled with liquid & pressure snapped into the liquid to force the old one out.
Berdan & Boxer primers have other internal differences also, but they complicate things further by having differing dimensions so you have to actually find the less common primers as well.
Because of the added complications the Boxer type are more "standard" or "reloadable" just because of the convenience factor. If you can only find Berdan-primed brass it can be reloaded, but you're going to put up with a few extra steps in doing so.
Conversions have been done, but they are strictly for low pressure loads & frankly, are to my mind more trouble than they are worth unless you're shooting some really unimaginably rare ammo & don't mind shotgun pressure level reduced loads.
Allan Quatermain: “Automatic rifles. Who in God's name has automatic rifles”?
Elderly Hunter: “That's dashed unsporting. Probably Belgium.”