Vivien wrote:
state schools is what normal schools are called, then there are private schools that are fee paying but don't have that extra status of the public schools (very high fee paying) - which are old established and people put the baby's name down at birth to get into them!
Adding a little bit to Vivien's piece: (can you say that in America?)
OK, if you were a child of a well-to-do or aristocratic family in the 14th or 15th centuries in England, how did you get your education? (There were no schools, and travel was difficult and dangerous.) Daddy arranged a private tutor for you, that's how. Like the Clerk of Oxenford in the Canterbury Tales, something like that, or a poor curate. He came to your castle or manor house (or he lived there full-time), and taught you Latin and Greek, and maybe some more. This was obviously limiting.
As population and wealth increased, so the 'public schools' came into being, still for the privileged classes, as they remain largely to this day.
Famous among those, Eton, Harrow, Winchester, Rugby, etc
These venerable institutions predated a state school system by several centuries. (in some cases) I believe Henry VIII was instrumental in founding some, presumably to reduce the influence of Church teaching.