der Schüler
student
A person, usually a child or teenager, who attends a general-education school.
Der Lehrer erklärt den Schülern die neue Aufgabe.
The teacher explains the new task to the students.

student / pupil
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student
A person, usually a child or teenager, who attends a general-education school.
Der Lehrer erklärt den Schülern die neue Aufgabe.
The teacher explains the new task to the students.

The word 'Schüler' (student / pupil) is directly connected to 'die Schule' (school). A Schüler is a person who attends a school in order to learn.
Die Schule organisiert einen Ausflug für alle Schüler.
The school is organizing a trip for all students.
The context makes clear which meaning is intended. Words like 'Klasse' (class), 'Lehrer' (teacher), or 'Fach' (subject) point to a schoolboy or school student. Names of philosophers or artists point to a follower or learner.
Mein Sohn ist ein guter Schüler in Mathematik.
My son is a good student in mathematics.
In the meaning 'Anhänger' (follower), the preposition 'von' (of / by) is almost always used to name the person or doctrine that someone follows.
Er gilt als wichtiger Schüler der Frankfurter Schule.
He is considered an important pupil of the Frankfurt School.
teacher
'der Schüler' and 'der Lehrer' both belong to school, but they have opposite roles. The student learns and attends class. The teacher teaches, explains, and gives assignments. Learners may confuse the words because both people are in the classroom. The important thing is the direction: the teacher gives knowledge; the student receives it and practices it.

Der Schüler fragt nach, weil er die Aufgabe nicht versteht.
The student asks a follow-up question because he does not understand the task.
Nach der Pause erklärt der Lehrer die neue Grammatik.
After the break, the teacher explains the new grammar.