Difference between question and problem in Korean
물음·문제

물음question
물음 means a question. It is used for something a person asks when they want an answer. In school, you can use it for a teacher’s question or a question on a test or worksheet. It is a simple word for something you answer.

문제problem
문제 means a problem. In school, it often means a question or exercise in a workbook, homework, or a test. You can also use it for a difficulty in daily life, like a problem with a computer or a ticket.
The difference
문제 is a problem or a test item. It can be something to solve or choose, not just something a person asks.