Differences between American and British English: student
In the U.S., a student is anyone who is studying at an elementary school, secondary school, or college. In the U.K., student means someone who is studying at a college or university. A child in elementary school in the U.K. is usually called a pupil. American speakers often use graduate student to refer to someone who has finished their bachelor's degree (=first degree) and is studying for an advanced degree. In the U.K., you would call this person a postgraduate.