In reality, both terms are horrible.
There is no deficit in attention, but rather an inability to prioritize and control attention.
If anything, you are trying to pay attention to too much.
I like to use the noisy diner example, I pay as much attention to the couple arguing in the corner, wondering how long the dude is going to remain on his phone when he has a beautiful date sitting with him, wondering what the back story of the eccentric-looking dude in the corner, trying not to stare at the cleavage tattoo next to me, and replaying the last meeting at work in my mind… as I am the person that I am talking with.
We actually have a test for this specific example, it is called “auditory figure-ground”.