From my understanding, the difference is in how much interpretation work you do. For mindfulness, you are trying to get at the raw sensation. There is no mountain range or forest, there is only the beautiful imagery in front of you. You actively try to inhibit any kind of pattern-recognition that abstracts away what you see and ideally see the trees for the forest.

Whereas awareness is allowing the pattern-recognition to function, in such a way that you notice when something is unusual. An aware person would notice a deer in the forest, and not get distracted by the different trees.