Correct? Yes. The first one could be answered with "I like jazz and rock and techno ..." The second one could be answered with "oh, I like jazz and rock and techno .... Any of those will do" effectively selecting one, as you suggest. . "what would you like? tends to mean one, now. Tea, please. "what do you like?" is asking about general preferences. Well, I'm felling down, so let's have blues. . So a waiter will say "What would you like?"

Hello Hong Ju! :) "What kind of music would you like? - If someone wants to find out what kind of music you would like to listen to - for your birthday, for weddings, parties, now or for some time in the future. Which genre of music do you like to listen to most? This question could relate to a particular genre of music. "What kind of music do you like?" This sentence is correct and it just indicates the question - what kind of music do you like to listen to, in general, it can also refer to a particular genre.

I don’t know the official grammatical definition as I am not an English teacher, but..... What do you like is just what you generally like in a broad sense. What ‘would’ you like is more subjective... Eg If I was young , I would like nursery type music If I was in a wheelchair, I would require access that didn’t have any stairway. It’s quite difficult to suggest examples, so I hope this answers your question? Mike