Custom cosmology. It's tied to the reason why devils and demons exist. The original fiends started as celestial beings of various stripes (just like there are currently multiple types of celestials). They rebelled and were cast from the heavens. They were cast in the general direction of oblivion. That isn't capitalized, in the way it is in Wraith, but is more a sense of "outer darkness" or "wailing and gashing of teeth". At the same time, the Abyss gets worse, as it gets deeper, so there may be something (nothing?) at the bottom.
Regardless, the devils could be considered the fallen who are more well adjusted, if you can apply that concept. The devils still hold out hope that they can win the War of Souls. By gathering sufficient souls, the very essence of creation, they hope to both blackmail the Creator force into reconciling and, if they're really arrogant, shift the balance of power to the extent that they can take over.
Demons, on the other hand, have given up hope of winning. They know they're screwed, at the end of ages. Instead of trying to win, they're engaged in a salted earth campaign to drag as much of creation into oblivion with them. Some of them are playing the long game to extend their own existence. Others want to speed the end as much as possible. Still others -- maybe the most disturbing -- want more to be created so there's more to be destroyed. Regardless, all are working from motives so alien to mortal thought that they may as well be insane.
Scholars speculate that there may be certain fiends or classes of fiends (loths?) that didn't actually fall, but were created to test other elements of creation to weed out those that were too badly flawed to be retained. The reasons given for this vary: an imperfect Creator seeking to cleanse itself, providing meaningful choices and true freewill, and more esoteric theories. If so, the implications would be significant -- there would be almost no chance of the fiends winning; even their fall was part of a bigger plan, from the very beginning.
With all the fiends circling the drain, so to speak, Hell can be viewed as the upper rim of the Pit, or even as the flat area around the hole. It's generally stable, if terrifying and oozing evil. The ninth layer of Hell sits at the lip of the precipice, ready to fall in. The Abyss, on the other hand, is the actual wall of the Pit -- a careening free-fall of malevolence to existence itself. As far as mortals know, the bottom of Hell is fully disconnected from the top of the Abyss. They're joined only by virtue of being evil. But, it's entirely possible that Hell could begin to slide into the Abyss, at the end times or if the devils ever gave up hope. It's unclear what this would beget, but it's not likely to be good.
Anyway, the specific rulers of the layers of Hell has rarely been a big concern. I really hated the 2E Blood War, so my baseline assumption is still the late 1E hierarchy. Honestly, everything to do with the lower planes since PlaneScape kicks the same spot of my brain as all of Lucas' messing with the original trilogy: just stop, already; it was fine as it was. The blurb in the 5E DMG isn't any more inspiring than anything else in the last 20 years.