"bitartrate of potash" (a deposit left during fermentation), late 14c., from Old French tartre, from Medieval Latin tartarum, from late Greek tartaron "tartar encrusting the sides of wine casks," perhaps of Semitic origin, but if so the exact source has not been identified; Arabic is unlikely because of the early date of the word in Latin. The purified substance is cream of tartar. Used generally in 17c. of encrustations from liquid contact; specific meaning "encrustation on teeth" (calcium phosphate) is first recorded 1806.
mid-14c. (implied in Tartary, "the land of the Tartars"), from Medieval Latin Tartarus, from Persian Tatar, first used 13c. in reference to the hordes of Ghengis Khan (1202-1227), said to be ultimately from Tata, a name of the Mongols for themselves. Form in European languages probably influenced by Latin Tartarus "hell" (e.g. letter of St. Louis of France, 1270: "In the present danger of the Tartars either we shall push them back into the Tartarus whence they are come, or they will bring us all into heaven").
The historical word for what now are called in ethnological works Tatars. A Turkic people, their native region was east of the Caspian Sea. Ghengis' horde was a mix of Tatars, Mongols, Turks, etc. Used figuratively for "savage, rough, irascible person" (1660s). To catch a Tartar "get hold of what cannot be controlled" is recorded from 1660s; original sense not preserved, but probably from some military story similar to the old battlefield joke:
Irish soldier (shouting from within the brush): I've captured one of the enemy.
Captain: Excellent! Bring him here.
Soldier: He won't come.
Captain: Well, then, you come here.
Soldier: I would, but he won't let me.
Among the adjectival forms that have been used are Tartarian (16c.), Tartarous (Ben Jonson), Tartarean (17c.); Byron's Tartarly (1821) is a nonce-word (but a good one). Tartar sauce is attested by 1855, from French sauce tartare.