This is a room drowned in euphemism. In some areas "going to the toilet" is the euphemism for the physical activity that takes place there, and might not therefore be acceptable in polite society. Toilet, bathroom and lavatory all mean basically a place to wash. Czech is fortunate in having a specific word for the room although it is itself a euphemism, meaning, I believe, a secluded place (like latrine in English)
Czech people may have an impression that "toilet" is a high-society word like "toaleta" in Czech and that is not the case. Especially not in America.
There are many synonyms and hyponyms with various level of politeness in Czech (see https://en.wiktionary.org/wiki/z%C3%A1chod).
For Jenda: "Do you want to go to the toilet?" is accepted here.