The sentences in common usage mean the same and are interchangeable, but there is a slight difference in nuance between the two if you want to look for it. When people make a 'comment', they put a little more time and thought into it. In contrast, a 'remark' is more an immediate response to something just said or done. Less an opinion is being made when you make a remark as you have not given it much thought ... you are just responding immediately to something said. So with your 2 sentences, while they largely mean the same, the 2nd can imply that his rude statements are more an opinion rather than something said with no thought.

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Without any further context, I would say that you are probably supposed to answer that a "remark" is a spur of the moment reply and a "comment" is a considered answer.