This is the crux of it for me also.Both seem to be exonyms though. Don't know how accurate the translation of the article is, but it tells that "Tartarias" on western maps correspond to "Hordes" on Russian maps. The name Tatar was made up by some German historian in Romanov Russia to bundle a lot of different Siberian people together. There was also a period of morphing of the maps - Tataria---> Tartaria.
To me it's all the same, one name calls them savages, while other means hell. From the stuff found on this forum it appears that neither are true.
Tartary, Grand Tartary, Lesser Tartary are names referring to a geographical area of land put there for good reason.
The Westerrn european peoples who would consume the maps,stories, journals, drawings/engravings/paintings/products of merchant adventurers were given a name they could relate to.
And equally important any merchant group seeking the exact source of another's product and on bein told inTartary they would set off along the silk road only to find there is no Tartary!
The Mongol Empire, The Uigyhr Empire, TheTang Empire, The Sogidians, The Bactrian Greeks and a plethora of smaller kingdoms argued, made peace, fought, rose up, faded away in a part of the world where the silk road traversed and few western people ventured.
The religions of the area morphed and rubbed up against each other but catholicism was not among them.
Here's a list of threads and articles which reveal all manner of goings on within the Tartary label. Maybe they can open some doors for some people, hope so.
View: https://mobile.twitter.com/cartographer_s/status/1483954508015230976
View: https://mobile.twitter.com/cartographer_s/status/1539348577469734912
View: https://mobile.twitter.com/cartographer_s/status/1546917528173158400
View: https://mobile.twitter.com/cartographer_s/status/1549453701047361536
Alexander's Cartographer's Newsletter
Then there are these inconvenient findings.
View: https://mobile.twitter.com/AquaPaadre/status/1578523033672687616