A charter school IS a public school. Charter schools are still publically funded and under the administration of public education personnel. The difference between charter schools and regular government schools is that charter schools have relaxed regulations in some areas in exchange for the promise of enhanced educational results, the specifics usually being laid out in the school's charter.
Yes it is a Public School but the states grant them the ability to set rules and regulations approved by the state. This school’s dress code was such. The parent also agreed when she put her kid in there.
I worked for MAPSA here in MI. It’s The Michigan Association of Public School Academies. In other words, charters.
We called our schools Charter Schools and the others District Schools.
Ah. The few charter schools in my area run like private schools. Uniforms, very small classes, and they can pick and choose who attends. They’re all, except for one, administered by private groups (a church, a local college) and unlike public schools, they don’t have to accept anyone.