* Private School: This is the broadest category. It simply means a school that is not publicly funded and therefore charges tuition. It encompasses prep schools and academies, as well as many other types of independent schools. Private schools can vary widely in their focus, religious affiliation, teaching methodologies, and student population.
* Prep School: A prep school (short for "preparatory school") is *a type of private school* specifically designed to prepare students for college or university. They often have rigorous academic programs, a strong emphasis on college counseling, and a wide array of extracurricular activities aimed at developing well-rounded applicants. They may also have a strong focus on standardized test preparation. Not all prep schools are boarding schools, although many are.
* Academy: "Academy" is a very broad term and can refer to many different types of schools. Some academies are private schools with a specific focus, like a performing arts academy, a military academy, or a science academy. Others might be publicly funded charter schools that operate under a specific educational model. Therefore, an academy *can* be a private school, but it doesn't automatically mean it is.
In short:
* All prep schools are private schools.
* Some academies are private schools, but not all.
* Private school is the umbrella term encompassing many types of schools, including prep schools and some academies.
The best way to understand a specific school is to look at its individual mission statement and curriculum. The labels themselves can be misleading.