A following question is the next question in sequence. It may have nothing to do with the questions it follows.
A follow-up question is related to the question, or question, that it follows. It may, for example, be different depending on the answer to the previous question.
Examples.
Do you have any children?
What colour is your hair? <- This question follows the first question.
Do you have any children?
What are their ages? <- This is a follow-up question.