A lot of this is accounting.
You don't need to buy chromebooks for pupils when they already bring their own tablets/laptops. It's not unheard that if there is some initiative requiring equipment (music, sports, smartboards) parents fund that initiative outside tuition costs.
Private schools tend to be controlled-admission and controlled-admission schools can have much narrower variance in skill level. The "dumb" kids do not swallow attention of the teacher and the "super-smart" kids do not get neglected. Richer parents can afford private tutors, closing the gap even further. On top of that, they tend to afford more time to coach their children in the right direction.
All of that costs a small fortune, but is not visible if you compare total state funding of public schools versus admission / tuition costs.