Ever wondered why in England the most prestigious private schools like Eton are called "public schools"? This idiosyncasy of the English culture has given rise to many a translation blunder. So translators, be aware, in case you find this term in an English text!
Here are the answers.
A public school, in common English usage, is a prestigious school which charges fees and is not financed by the state. In Scotland a public school is a state school, a fee-paying school is a private school. It is traditionally a single sex boarding school (although many now accept day pupils and are coeducational). The majority date back to the 18th or 19th centuries, and several are over 400 years old.
The English usage is in direct opposition to what any foreign English speaker would expect. In English usage, a government-run school (which would be called a 'public school' in other areas, such as Scotland and the United States) is called a state school.
The term 'public' (first adopted by Eton College) refers to the fact that the school is open to the paying public, as opposed to a religious school, which was open only to members of a certain church. It also distinguished it from a private education at home (usually only practical for the very wealthy who could afford tutors).
Source: https://en.wikipedia.org/wiki/Public_school_(UK)
In England, originally, A grammar-school founded or endowed for the use or benefit of the public, either generally, or of a particular locality, and carried on under some kind of public management or control; often contrasted with a 'private school' carried on at the risk and for the profit of its master or proprietors. In modern English use (chiefly from the 19th century), applied especially to such of the old endowed grammar-schools as have developed into large, fee-paying boarding-schools drawing pupils from all parts of the country and from abroad, and to other private schools established upon similar principles. Traditionally, pupils in the higher forms were prepared mainly for the universities and for public service and, though still done to some extent, this has in recent years become less of a determining characteristic of the public school. It is a general feature that order is maintained and discipline administered to a great extent by the elder pupils themselves: hence the prominent notion in such phrases as 'a public school education' or 'the public school ethos', which are today taken perhaps more broadly to connote the general qualities which the discipline and spirit of the public school are held to impart.
The Latin form appears in the 12th c., and is frequent from the 14th c. as applied to an endowed free grammar-school. The English form public school is known from 1580, and was no doubt used earlier. Down to the 18th c. it was very generally opposed to "private school', and education in a "public school' was also contrasted with education at home under a tutor The term was officially used in 1860 in the appointment of a Royal Commission, and in 1867 in 'An Act for the better government and extension of certain Public Schools'. As this act applied to the ancient endowed grammar-schools or colleges of Eton, Winchester, Westminster, Harrow, Rugby, Charterhouse, Shrewsbury, these have sometimes been spoken of as 'the Seven Public Schools'; but the name is generally used to include these and numerous other large schools, ancient and modern, of similar organization, which are not separated by any definite line from other endowed schools that depend upon a more local constituency.
Source: Oxford English Dictionary