For text match problem, what is the different between question-question match and question-answer match? I know question-question match is a text similarity problem.

What about question-answer or question-doc match? It is used in information retrieval.

question-question match is indeed text similarity. But how do you define question-answer similarity? 

Thank you!!
You can refer to the paper "A Deep Look into Neural Ranking Models for
Information Retrieval" to get more discussion about different matching tasks.