I do focus on the music, which sometimes is counterproductive.

Probably more. Depends if I focus on the beat, the melody, the lyrics or vibe of it, otherwise it's just in the background.

I'm always focused on something, whether it's my own thoughts, something I'm doing, something I'm watching or listening to, etc. One time a girl saw one of my graduation photos and said, "you look like you're very sure of something." I was just sure of whatever I was staring at at the time. If listening to music I'm focusing on the music. If I'm doing something else while the music is playing I'm likely to miss the music and have to play it over again if it's something I want to listen to (e.g. for the first time).