For my own part, I prefer to think in terms of physical differences of objects, moreso than spectral classifications-- though I know the latter generally is an essential step in achieving the former. So for me, the key question is, what kinds of different physics can happen near the bottom of the main sequence that we might want to think about, and how can that different physics connect with spectral differences?
I don't know the answer, but I think a key type of new physics that "ultra-cool dwarfs" connect with is the possibility of having a very low-mass dwarf that is not fully convective. The usual idea is, pre-main-sequence stars start out fully convective, because they are very large and even though they are red, their luminosity is too high (because of their huge surface area) to be carried radiatively, so convection has to pick up the slack. But as the star contracts, its luminosity drops, and its interior also gets hotter, so for both those reasons, radiative diffusion becomes better able to carry the load without as much help from convection. So stars like the Sun become less convective before they get to the main sequence, and stay that way.
But not the cool dwarfs. It turns out that radiative diffusion is very sensitive to the star mass, so low-mass stars are not very good at having radiation carry their luminosity. Hence "red dwarfs" stay fully convective all the way to the main sequence, and stay that way even once fusion initiates. However, and this is the interesting thing about "ultra-cool dwarfs" on the main sequence, as H is converted into He, radiation becomes better able to carry the luminosity. (What happens is a little counterintuitive-- the star expands because it literally has fewer particles in it, so it must reach a lower overall pressure scale and hence a weaker gravity scale, and a more expanded star at the same fusion T carries more photons in it, which carry the luminosity as they diffuse out, and they might encounter less opacity to block them as well.) The bottom line is, at some point during the conversion of H to He, radiative diffusion might be able to carry the luminosity of the star (I don't know just when), so the star is no longer fully convective.
This changes the evolution of the star, because if the core is not convective, it starts to pile up He in the center. It also means the entire star is not able to be converted into He, as would hold if the star stayed fully convective. I'm not sure what all the evolutionary ramifications are (and note they have not been observed because these stars have not had time to do this in the entire age of the universe), but it certainly makes for a very interesting object! (The sources you cite talk about evolving into "blue dwarfs", for example, but I'm not sure exactly how that happens, there must be quite a lot of interesting physics in these objects that the universe has never yet seen!) Thank you for bringing attention to these fascinating objects.
