¿Cuál es la diferencia entre Ich höre gerne Musik. y ich mag Musik zuhoren. ?Puedes dar oraciones como ejemplo.

The first one is correct, the second one isn't, because "mögen" (in the sense of "to enjoy") requires an object. You could write "Ich mag es, Musik zu hören" ("es" becomes the object) or "Ich mag das Musikhören" (you have the noun "Musikhören" as object), both meaning "I enjoy listening to music", but while correct, both feel unnecessarily complicated to me, and "ich höre gern" is much easier. But people don't always use correct German, and you will find often that when talking, people use "mögen" also in the sense of "möchten" (= would like), and thisworks not only with an object, but also with a verb. For instance, "Ich möchte Musik hören" = I would like to listen to music (now) would be correct. People might also say "Ich mag Musik hören", which is not really correct, and they might use it either in the sense of "would like" or "to enjoy (in general)", and we have to deduce the exact meaning from the context. I suggest that you avoid it, but be patient if someone is actually using it.