So What is the difference between

[Whoooosh]

Private schools and Public schools?(other than fees of course).

How does a school,or can they,become a Public School?

I think it is to do with whether the school is the the Headmasters' Conference, which is a group of the posher private schools.

might be wrong

It's whether or the head teacher is a member of the Headmasters' & Headmistresses' Conference.

Well that is interesting-how do they become mebers then-are they really better than any other head teachers?

Tbh I think most people use the terms interchangeably. Chambers Dictionary says public school = 'school under the control of a publicly elected body' (so state school) or 'an endowed classical school for providing a liberal education for such as can afford it ? Eton, Harrow, Rugby, Winchester, Westminster, Shrewsbury, Charterhouse, St Paul's, Merchant Taylors' etc.'

My school referred to itself as an independent school but then it was for girls, obv.

Public schools are usually for boys (although many are now co-ed) and 13+ entry.

Public schools are more exclusive than just being members of HMC - they are generally boarding schools for 13-18 year olds. Schools such as the GPDST High Schools and equivalent day schools for boys (e.g. Manchester Grammar, Perse, RGS Guildford etc) are known as Independent Schools now. They were previously known as Direct Grant schools, back in the days when some places were government funded.