There is not much difference in the sense of a school or learning setting. Exam is a larger test, like a final exam. In order from smallest importance to biggest importance it would go: quiz, test, exam. Exam can also be used when going for a medical checkup. Like a dental exam or a physician's (doctor) exam. In this sense it is not a "test" but more an examination of the condition of something.

Usually a test is less important to the student's final grade and less comprehensive (it might cover a chapter or two of a book or a week or two's worth of material), but an exam covers more material (perhaps even everything covered during an entire semester) and counts more toward the final grade.

Same thing.

Very little. In the United States, the words "quiz," "test," and "exam" (short for "examination") are rough synonyms, but an "examination" is usually more important than a "test," and a "test" is more important than a "quiz."

Hi Camila! Generally speaking, an exam is of more importance and more formal than a test, and a test usually tests a certain topic or a few topics while an exam is more broad and may test more topics . Hope this helped!