Yes exactly. The "mindfulness" designation is a recursive one, where first you are mindful, then you are mindful of that which is mindful, and all the way down.
My problem with these terms is there's no chance of not being mindful. It seems to refer at once to both immediate awareness of surroundings and kind of meta self-awareness. You're in the present moment no matter what you do but redirecting focus seems to help get a grip on emotions.
