Just a small thing to add:
Schüler can be also used to mean an "Azubi", a person who is learning a profession either thru a school or apprenticeship. It is however a regional thing and on some areas they are rather called a "Lehrling" or just "Azubi".
For example a person how is studying (using the word in the English sense) to become a nurse in a nursing school is often referred (at least here in South) as "Pflegeschüler".
In English they would be called students, in German never.