What is the difference between give an exam and take an exam?

"Give an exam" is a statement of command or action where there is someone providing either a written, oral or actual test to a person or group of persons. "Take the exam" is also a statement of commend and an action, depending on how you will use on a sentence, when someone is asked to take a test which can be through written, oral or exam.

Below are examples where two statements are used as actions:

Teachers give exams to their students.

Students take exams