"State" school are the free, government run schools. "Public" schools are typically fee-paying, and are named so because when they were founded, anyone who paid

"State" school are the free, government run schools. "Public" schools are typically fee-paying, and are named so because when they were founded, anyone who paid could send their children there, rather than it being restricted by class or religion. They were "public" because the general public could send their kids there.