I expect that people who mention MUDs largely do not expect anyone to know what they are talking about, since these games have nearly always been tiny and nowhere near even nerd pop culture. At least this has been my experience -- so I will prefer to say "I am playing this game called Hesperia/Achaea/Discworld/whatever, which is like a text-based RPG" and avoid even the "MUD" terminology.

Further, I expect an even smaller subset of people who have played MUDs are aware of the 'distinct genealogical lineages' you describe. As someone who spent my teens browsing mudconnector and dabbling in lots of random MUDs listed there, I started hazily noticing patterns in structure, design, mechanics, and even networking to some extent, and suspecting that certain games existed within specific 'traditions' of MUD development or even used similar libraries or frameworks, but I didn't have the context or curiosity to dig deeper.

Like everything, this can be modeled as a funnel: of the relatively small number of people on planet Earth who know that MUDs exist, only a tiny fraction has even connected to one, an even tinier fraction of those spent meaningful time on one, and an even smaller number of these who have thought to contextualize and taxonomize what they were played

Anyway, I am curious what level of specificity would you find normal?