There is a very extensive set of public and private universities, colleges, and community colleges. Anyone who really wants to get a college degree can get one somewhere. There is a very wide range of costs even for public schools (public schools are all state-run; there is no network of federally owned colleges for general education).
For example, when I was entering college, I had a wide range of choices, from the local state university, whose tuition was about $2,400 a year, a nearby state university of a slightly higher quality whose tuition was $5,000 a year, to a more distant, nationally reputed public school in another state whose tuition was about $20,000 a year. Private schools, of course, can cost much more.
By the way, in America, an educational institution at any level can be referred to as a school. Even a doctoral degree student or a university professor will refer to his or her institution as “school.”
Usually, an institution with the word “university” in its name is a very large institution that offers degrees in every discipline and offers a range of doctoral and master’s degree programs. A univerisity is divided up into units that have names like “College of Liberal Arts,” “College of Science and Mathematics,” and “School of Medicine.” These colleges and schools are divided up into departments (I think they’re called “faculties” in the U.K.).
An institution with “college” in its name is usually smaller than a university (but not necessarily – e.g., Boston College and Boston University are both fairly large institutions), and may offer a smaller ranger of subjects of study (but, again, not necessarily). Both colleges and universities, though, will offer several different bachelor’s degrees.
Informally, the terms "university, college, and school are to a large extent interchangeable. Basically, it’s up to the institution what appellation to choose and you have to be careful about how you refer to it.
For example –
State University of New York at Buffalo – not New York State University or Buffalo State University
Indiana University – not University of Indiana
Miami University is a public school in Oxford, Ohio. The University of Miami is in Coral Gables, Fla.
The word “state” in the name of an institution almost always indicates that the institution is a public school. Not always, though. For instance, what used to be called Towson State University is a private school. A name including the naen of a state or city might or might not be a public school. You just have to know. For example, Pennsylvania State University, the University of Michigan, Ohio University, Miami University, and Ohio State University are all public schools. However, the University of Pennsylvania and the University of Dayton are private schools.
Most states have an extensive network of public schools. In California, there are two parallel systems – the University of California system and the California State University system. Each of those systems has dozens of campuses around the state and they all have names like University of California at Irvine, University of California at Los Angeles, etc.
Ohio also has an extensive public university system, but there each school has its own name – Ohio State University, Ohio University, Miami University, Wright State University, University of Cincinnati, Bowling Green State University, Cleveland State University, Kent State University, Shawnee State University, University of Akron, University of Toledo, University of Findlay, and Youngstown State University.
Kindergarten is not compulsory. Parents may choose to delay registering their children for school until first grade, when they are 6 years old.
If you complete a course at a two-year institution, you are awarded an “associate’s degree.”