Tartar can be a deposit on the teeth, or in wine, but obviously none of us can be either of those.
No, the sort of tartar that's relevant here is a person who keeps very strictly to the rules and is ferocious enough to make everyone else stick to the rules, too.
In the Olden Days it was hospital matrons who were especially known for being tartars, which was probably a good thing for infection control if not much conducive to comfort. The word tartar tends to be used in a grudgingly admiring way: tartars are a nuisance to everyone, but they're effective at making everything run really properly.
They're in charge, and everyone knows it.
I can't say that tartars were ever in fashion, exactly, but they're definitely out of fashion, now. Giving people orders is out of fashion: nowadays we make tend to make suggestions laced with emotional blackmail.
Is that a kinder way to proceed?
Or is it reasonable to be resentful that our emotions aren't completely our own business?
Thing Perhaps Not To Be Today: a tartar. The original Tartars, or Tatars, were the followers of Genghis Khan. He was throwing his weight around in Europe in the Middle Ages. (Some of their descendants still live in the Tatar region of Russia, but I'm sure they're all charming.) The word came to English from the Old French Tartare (the Tartars are said to have tenderised their raw steak by putting it under their saddles and riding about on it all day, which gives us the name of the raw meat dish steak tartare), from the Latin Tartarus (a word connected with the Underworld), from the Persian Tātār.