This some fantastic reading. Some insightful, some hilarious: "Steak tartare was not invented by Mongol warriors who tenderized meat under their saddles."
Maybe a confusion of tartar the sauce with Tatars the central Asian nomads?
There’s possibly something there though, even if the steak tartar version is incorrect. Bret Deveraux claims the aim was to preserve meat into a kind of jerky: “On the move, meat could be placed between the rider’s saddle and the horse’s back – the frequent compression of riding, combined with the salinity of the horse’s sweat would produce a dried, salted jerky that would keep for a very long time.”[1]
His stuff is very well sourced, but also he’s self-admittedly talking outside his area of expertise there. So who knows.
I had always assumed they had the same etymology. It didn't help that in Spanish all of these words maintain the 'r' between the 'a' and 't': tártaro, ra, Tártaro, Tartaria.
Although I don't know if the Wikipedia article should be trusted, since the English version one (Tartar sauce) states: "The word Tartar is a Turkic word that is the name of Tatar people."