So…both mean ‘question’, so what’s the difference?
This means both ‘question’ or ‘problem’. If you want to say ‘I have a question’, this is what you would use. For that you would say:
저는 질문 있어요
I have a question (formal)
나는 질문 있어
I have a question (informal)
You could also drop the ‘I’ from the sentence and just write:
So, you would not use this word to say ‘I have a question.
문제 있어요 is weird.
문제 is also ‘question’, but it is the kind of question that would you find on an exam.