Attention management is the ability to control your distraction and maximize your focus, to be present in your moments, engage your flow, and unleash your genius.
At its heart, attention management is about learning how to focus your attention, breaking free from all the things you're constantly distracted by or reacting to.
Time management is a process by which one consciously keeps track of the amount of time they spend on each of their activities, in an effort to increase efficiency when it comes to usage of time.
What if you stopped worrying about how you spent your time, and instead, considered how you spent your attention? I'll tell you - you'd get more done and be happier!
Someone may spend their time sitting in a chair, but where's their mind? Are they thinking about the person sitting nearby? Are they brainstorming business ideas? Are they pondering on the things they're thankful for? Are they pouting about their bad luck?
The critical choice we have repeatedly in life is where to direct our attention. Some one might argue that this is implied in "how we spend time", but when I hear "spending time", I think of actions - eating, sleeping, going to the pool, writing, reading, sitting in a chair, etc.