Wiktionary says контрольная работа is a "short" test at school. Would that be like what we would call a "quiz" in America? That might be a short test at the beginning of class with 10 vocabulary words or something (sometimes a quiz is a surprise, called a "pop quiz"), while a "test" or "exam" would typically be a test that takes the entire class period, covers at least a chapter's worth of material, and might have different types of questions (multiple choice, true/false, essays, etc).
Latest response ever from a European. Generally, a контрольная работа involves what germans would call any 'Leistungsnachweis', that is to say proof of work and the ability to work (hence the name in Russian). It is a general term that may cover any way to determine a student's ability to get stuff done. Can come in form of a written test or short oral quiz.