This is the first time I hear of this (https://xkcd.com/1053/).

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.

Here there are 3 different etymologies: https://dle.rae.es/t%C3%A1rtaro and here there's another one: https://fr.wikipedia.org/wiki/Sauce_tartare

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."