They run by the respective state government to offer free education for year 1 to 12 education with a materials or services charge in some cases. They are further run in two separated forms – open and selective. Open schools accept all people at the suitable age in a defined area while selective schools have some extra requirements for a student to entre.
They are mainly Religion-based systems of education operated by churches. Some of them are independent schools (well known as protestant grammar schools) which mean they can accept students regardless their religion. They usually charge high fees although they vary from schools.
In some of the time, most of the people believe that private schools can guarantee academic achievements and bring a bright future in later life. However, nowadays there are lots of arguments to against this assumption.