Private schools charge tuition. Private schools do not receive tax revenues, but instead are funded through tuition, fundraising, donations, and private grants.
Private schools are selective. They are not obligated to accept every child, and in many private schools admission is very competitive. Private schools do not have to accept children with special needs, and many choose not to (although there are a small number of private schools specifically designed for special needs children). As a result, most private schools do not have special education programs or teachers trained to work with students with severe special needs. Private schools will try to help all the students they admit, but extra resources may also come at an additional cost.
Private schools are not subject to as many state and federal regulations as public schools. Since private schools are funded independently, they are not subject to the limitations of state education budgets and have more freedom in designing curriculum and instruction.