Listening to songs means listening to songs. Music here refers to music in general, without specifying which song or category it is.

Example:

Some people like listening to music.

Others like listening to music.

We can listen to music on the radio.

We can listen to music on the radio.

Listening to music is also listening to music, but the music here is specific, such as a certain song, a certain category and so on.

Example:

Who can tell me why I can't listen to music in my space?

Who can tell me why I can't hear music in my space?