I’m not tremendously familiar with the “Lizzy McGuire” timeline but High school students around 11th grade begin to think about where they might want to go to college. There are many, many options, from small schools of 2,000 to enormous ones of 40,000. They cost different amounts of money, provide different levels of financial aid to needy students, are known for different types of curriculum, and are more and less competitive. Many factors – including grades, entrance exams, coursework, activities, volunteer work and more – go into whether you can get accepted into a particular college/university. Because there are so many schools, they are all so different, and many students aspire to travel far from home and live full-time on campus, it is a stressful decision making process.
Most students begin college around the age of 18, depending when their birthday falls. Most 18 year olds are eligible for, and possess, a driver’s license. However, most students beginning the process of applying for college, are about 16 and only just becoming eligible to apply for a learner’s permit or limited driver’s license (in many states you can only get a restricted license at 16 - no other teens in the car, no driving at night, etc).
Some schools are privately operated, others have taxpayer funding and preferentially accept students who are residents of the state they are located in (“state schools”). State schools accept students from out-of-state for a higher tuition, which is still usually cheaper than top private schools. Some state schools are extremely competitive and prestigious, others less so. Not every state has a prestigious university of nationwide renown, but most states have a well-regarded university and/or college, some middling universities or colleges, and a couple that are kind of crappy. As well as a large system of 2-year community colleges as noted above.
Some of the more famous state schools are the University of Michigan, The University of Virginia, and the University of California - Berkeley. Some of the more famous private schools are Harvard, Brown, Oberlin and The Massachusetts Institute of Technology (MIT). There are many famous public and private colleges/Universities.
For historical reasons, a few universities are known by the name [something] College, such as Dartmouth College (private) and The College of William & Mary (public) but they are exceptions. Most places known as [something] College are actually undergraduate colleges. “College” as others have noted, is the blanket American term for undergraduate education.