British private schools (Known as public schools because...British)

I am not sure, but I have a reason I think this is. In England, private school is a school so private it's not open to the public. Like schooling you get from a private tutor. Maybe your homeschooler pooled resource thing that you do in America.

Public schools are open to the public. You have to pay, and they don't admit everyone -- even rather nearly the opposite of that -- but it's not "private" either.

The US's history is different. Of course there were always some places to get an education, but as far as where anything resembling regular people would go: there was at first nothing. Then there were public schools. Private schools only came later in elementaries. Universities are a bit different.

British private schools (Known as public schools because...British)

I am not sure, but I have a reason I think this is. In England, private school is a school so private it's not open to the public. Like schooling you get from a private tutor. Maybe your homeschooler pooled resource thing that you do in America.

Public schools are open to the public. You have to pay, and they don't admit everyone -- even rather nearly the opposite of that -- but it's not "private" either.