Answer:
Public schools are essentially free education. They have more teachers, more students, etc. However, public schools are very expensive because they provide, in most people's opinions, a better education. In private schools the classes are a lot smaller and there are less teachers, which makes the teaching more focused and students receive more individual attention. Private schools have higher standards and usually have school uniforms. They also may or may not have religious affiliation.
Actually, public schools are not 'free' education. The word 'public' is confusing, because they are not public in the way state schools are. They are a form of private education and are certainly not free. Public school fees are well over £20,000 per year, depending on the school. Schools like Eton, Harrow, Wellington, Tonbridge, etc, etc are examples of public schools. As in the para above, the class sizes are smaller than in state schools. But remember, if you go to a public school you will be educated privately, despite the name!
Actually, not true. One does not necessarily get educated privately. And public schools are absolutely NOT over $20,000 per year- I don't know who edited the answer above but it is not correct. By the way, this is America, buddy. We're not in England.