The technical definition of a private school
The State of Wisconsin offers a typical look at private schools from the regulators' perspective: "The statutory definition of a 'private school' allows for some variation in curriculum and organizational structure. However, numerous state statutes and administrative rules affect how a private school can administer curriculum, employee regulations and protections, student health services, facilities, enrollment reports, pupil records, special education, and transportation."
While private schools are subject to all applicable local, state and federal laws and regulations governing the business side of things, the essence of a private school which is its curriculum and how it chooses to teach that curriculum is essentially in the school's hands. That's why you will find so many reilgious schools emphasizing their religious instruction. And they can do that with impunity because they are private.
Most private schools are incorporated as non-profit entities with the specific purpose of operating a school covering specified grades. Most private schools have been given tax-exempt status by the IRS under 501 (c) (3) of the tax code.
Funding for private schools
Private schools are funded by tuition fees, income from endowments and gifts. Public schools are funded for the most part by public funds at the local, state and federal level. A very small percentage of public school operating funds come from foundation grants and private donations.
The essential characteristic of private schools is that they are unique. No two private schools are exactly the same. They may perhaps use the same approach to teaching and philosophy but they are unique. Each school's governing body determines what happens in the classroom, when it happens, where it happens and when it happens.