No, the difference isn't music vs. other sounds....聴く(also commonly seen in it's noun form as chou in combination with other kanji) is more like "hear" or "hearing" in an auditory sense. There is a subtext of listening closely or paying attention such as 聴き取り, but I still think 聞き取り is more natural in this case. Maybe this is the sense in which it is used with music, I'm not sure.