Note in some European contexts (like UK) "public school" means something more along the lines of "private school" in the US. They have selective admissions, there's usually tuition, etc.
https://en.wikipedia.org/wiki/Public_school_(United_Kingdom)
> The schools are "public" from a historical schooling context in the sense of being open to pupils irrespective of locality, denomination or paternal trade or profession or family affiliation with governing or military service, and also not being run for the profit of a private owner.