Public Education vs. Public Schooling

Neal McCluskey on the difference between "public education" and monopoly of government-run schools:

Fortunately, there is a term that does strongly imply a system in which government provides the public not just with the means to obtain an education, but schools themselves. It’s called “public schooling,” a term I use repeatedly—and intentionally—in my piece attacked by Carey, and a system that, as I wrote, is very much at odds with basic American values.