So how are public schools different?
In Italy public schools certainly don't have individual lockers for students 99% of the time. Most of them also don't have big dining hall, at best they have a very small stand or bar where you can grab sandwiches and small snacks for the mid-morning break (at 10:30 a.m. if I don't remember wrong).
Especially since you have lots of homework to do everyday (at least 1 or 2 hours of homework at home per day and I'm being generous, usually it would be a lot more) in the afternoon at home, so you have to carry back home your stuff (books and notebooks). So it wouldn't make sense to have individual lockers where to leave your stuff at school. Many public schools wouldn't also have the space to accomodate lockers for each student.
In mine instead (which was private and quite an exception here in italy) we did 80% of our homework inside school in the afternoon.
Nearly all of of them don't have proper auditoriums and they certainly don't have student clubs that organize events, shows or music.
Also students don't stay inside schools at late afternoon. usually they go back home at 12:30 or in certain selected days at 1 or 2 pm (and this doesn't always happens; mostly in the last two years when there are more weekly hours and even then only in 2 or 3 days of the week not everyday) with no real lunch break; thus they don't have break for lunch, you eat at home usually when you go back. They have a small 15 minute break for snacks at 10:30 am usually and then another one (still 15 minutes) for those days when they stay till 1 or 2 pm. You then eat proper lunch after you go back home.
They certainly don't stay till 3-4 or 5 pm with optional activities. Usually there aren't any extra optional activities or clubs in the afternoon or at least it's pretty rare.
A few of them don't even have internal gyms and they go to external gyms nearby (with a rented bus) for their physical education, and those public schools who have gyms have 1 at best, usually indoor and I have never seen them having outdoor fields for P.E. or football or outdoor sports (meaning inside the school).