Back when I was at school, we had red slips and gold slips. 1 red slip was fine, 2 was a warning to parents and 3 meant your house lost 10 gold slips. Gold slips were "treats" like extra playtime etc so it's the classic "you're letting yourself and everyone down" scenario.
^This.
And it still happens. At the last two schools I worked at before I retired (girls' independent), the Deputy Head might hold a detention session once every 3 weeks or so, but only if necessary...
We had a system of house points and order marks. House points for good work, obviously, but geared mainly towards the younger girls. I think Y10 and up were a bit embarrassed if they got one!
Order marks came in two varieties - work (for late homework, etc.) and conduct. It was very rare to give a conduct order mark. During house meetings, the total number of order marks during that week was read out. No names, of course, but any girl who had got an order mark knew she was letting her house down, because order marks cancelled out housepoints.
Here's an example of something which might have warranted a conduct order mark but didn't. A mobile phone went off in my class. I just looked at the girl. (So did everyone else.) She went pink, rummaged in her bag to turn it off, and apologised both profusely and genuinely. No other punishment seemed necessary.
Order marks were handed to the form tutor to be passed up the chain. This involved a bit of extra work for the form tutor. I once told my Y9 form group that if any of them dared to get an order mark I would give them another as punishment for the extra workload. There were very few order marks that year!
But the big question is, why the difference? Is it because independent schools have more involved parents who are paying extra, or because senior management insists on high standards, or perhaps because such schools tend to be smaller (we had 400, including sixth-form) so most teachers know most girls by name, even if they don't teach them.
I really don't know.