[simeonf]

You are factually incorrect.

In North American usage a "public school" is a school open to the public and run on public funds (tax monies) instead of funded by charging students for access.

A charter school is just an independently run public school. Some are run by parent companies that are for-profit corporations running multiple schools. Some are not. I have a daughter enrolled in a charter school started and run by teachers and parents. No parent corporation is involved and it shares facilities amicably with a traditional public school.