I hope this makes sense, I feel kind of ramble-y...
Self awareness to me, is more of a conscious effort than anything. I don't believe that in general people can just BE completely self aware at all times, the ego gets in the way too much. But you can make an effort to evaluate why you react to certain things the way you do, even if you can't always see it in the moment. I guess I could define it as an effort to understand yourself on a deeper level rather than just accepting your thoughts, actions, and reactions at a face value and not questioning them. Someone who questions those things, to me, is making an effort to be self aware. A person who does not do this regularly, in my opinion, would not be very self aware.