A class quiz is a short quiz (that may feature multiple-choice questions or other kinds of questions) that the instructor in a class administers to students. Class quizzes may be take-home, in-class, or mixed (for instance, students are allowed to work at home but are given some time to review solutions in class). Students may or may not be allowed to discuss individual questions with one another.
Class quizzes differ from homework assignments in that the questions are generally at a harder level and are intended to serve a role that combines diagnosis and assessment. Homework assignments are generally intended more to make sure that people get appropriate practice with the material. Nonetheless, the distinction can be blurred in a variety of circumstances.