"Bathroom" and "restroom" are only used in American English. In other English-speaking countries, a bathroom contains a bath, and a restroom sounds like somewhere to go if you're tired.
"Toilet" is also a euphemism, it's Middle French for a type of cloth.
So is "lavatory", it means wash room.
I can't think of a word that isn't vulgar or a euphemism.
"Toilet" was by etymology a euphemism, but is no longer understood as such. As old euphemisms have become the standard term, they have been progressively replaced by newer ones, an example of the euphemism treadmill at work.
Washroom. Lavatory. Outhouse. Mens' room. Little girls' room room. Potty. Half bath. And many more (mostly NSFHN).
I suspect there's a deep reason for all the different words, probably because of the basic nature of what goes on within such rooms. I wouldn't be surprised if other languages have the same profusion of synonyms.
If you're in public and ask for a bathroom, it's assumed that you are looking for a toilet and not looking for a bath. I have never had to ask for a place with a bath in public - if I need a bath then I'm at a house or a hotel where I can find it.
Interesting. In my part of the world a bathroom must contain either a shower or a bathtub and a toilet (or a WC) must contain a toilet bowl. In the article the word toilet was used in the title, switching to the "bathroom" in the text was confusing.
Aren't the bathrooms the places where somebody can bathe?