'State school' is used to refer to state (as in United States) funded university or college. This may not be common across all regions though. Private schools for pre-university students are not that common in my area, which I assume has something to do with the specificity of the term here.

Note: I think I was less than clear. In my area 'state school' is a way to refer to university or college that is primarily or entirely paid for by state government.