Hmm, I'm glad to see your inquiring about the American school system. Perhaps the word pupil is used more frequently in Europe to describe children that are in school. I'm not certain.
Typically, it's structured this way (names are adjacent):
1. Elementary - elementary students
2. Middle School - middle school students
3. High School - high school students
4. College - college students
Pretty simple. Common, everyday English doesn't use too many sophisticated terms to classify one's education level.
There are terms such as secondary and post secondary that can be associated with two of these tiers. Secondary is often another way of saying high school. Post secondary is a term referring to those at the university level.
In general, you refer to everyone enrolled in school as a student. You COULD refer to college students as collegians, but professional organizations tend to use this word more so than the average American citizen.