so I says to myself, "tsuwm, you *could look it up"... well, as luck would have it, this one isn't as simple as it looks; I've found three(3) general themes for 'public school';
1. an endowed secondary boarding school in Great Britain offering a classical curriculum and preparation for the universities or
public service [M-W]
2. In England the term was originally applied to the grammar schools endowed for the use of the lay
public; it has come to be used for the famous endowed preparatory schools that now charge tuition, e.g., Cheltenham, Eton, Rugby, Westminster, and Winchester. [encyclopedia.com]
3. a
posh {it's very weird how these threads tangle} private school (Eton, Harlow, etc.) [British Slang Glossary]
...so I guess I'm sure I still really just don't know.