I listen to music : 나는 노래를 듣는다, 나는 음악을 듣는다.
I'm listening to music : 나 지금 노래(를) 듣고 있어, 나 지금 음악(을) 듣고 있어.
you can speak these sentences leaving out (를) and (을), it is informal speaking, but In the writing, you have to write these together in the full sentences.
It is style of people that tell difference between 노래 and 음악. In my case, 노래 is friendly with younger people so It is popular now and 음악 is more inclusive word but more older music is likely pointed in this word. Maybe classical music is classified as here.