I speak from the point of view of a mathematician. Mathematicians use the words frequently and interchangeably. There is absolutely no difference. When they assign a problem (= question) as homework to a student, they refer to it as an "exercise". The mathematician uses the word "problem" in a way that no other person does. For most people, "problems" are bad things that you want to avoid. The mathematician, by contrast, is constantly searching for interesting problems. The solution of such problems is the purpose of their lives. A problem becomes "interesting" if you do not know its answer -- especially if NOBODY knows the answer -- and discovering its solution will prod you to gain valuable insights. Those are the problems you want to think about. You cannot look up the answer because nobody knows it. You cannot ask a machine for an answer. You can only think about it long and hard, talk to other mathematicians about it, and read what others have discovered about related questions. That process is called "research". Unlike many other people, when mathematicians cannot figure out a solution to a problem, they admit defeat. That is a remarkable characteristic in a world where for so many people not knowing an answer is no impediment to offering one anyway.

I think that they are often used interchangeably, but a "Math problem" is usually something you have to solve. It’s like a puzzle in math where you need to find the answer. For example, "Solve this math problem: 5 + 3." While a "Math question" can be a question about anything related to math. It might be asking for an explanation, like "What is addition?" or it could be asking you to solve something, like "What is 5 + 3?

This is a very interesting situation, it was mind blowing to me to realize that in Chinese both problems and questions are 问题. In English we make a difference. A problem is something that you need to solve hence a mathematical problem because it has a solution, or I have a problem with my car, or my neighbor has a problem with his stove. A question requires an answer but it’s not necessarily a solution, How can I learn Chinese faster? It’s a question, and you can answer in many different ways but none would be an exact solution like a mathematical problem. In math we use both problem/question like in Chinese. I hope it helps 😉

"Math problem" is a common collocation, but "math question" simply isn't. It's possible that someone could have a question about math and refer to it as a "math question', but it's not something that natives say regularly. On the other hand, we often talk about "math problems." By the way, with either "problem" or "question" you need an article or some other determiner before the noun when it's singular ("a math problem" or "a math question.")

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