It's all in the way a person uses the words. They can mean exactly the same thing, or they can imply slightly different things. It depends on the person using the words and their vocabulary. For me personally, I usually mean them exactly the same. I don't make a differentiation. Some teachers make a differentiation, they say mindfulness is more "this", and awareness is more "that". If you're confused with the teacher, ask them about how they define the words, but for me, they're basically the same thing.
There is, though, a difference between "mindfulness" and "Mindfulness"; or "awareness" and "Awareness"; or "mindfulness" and "Awareness"; or "awareness" and "Mindfulness", depending on whether we mean a "small" mindfulness or a "big" one; a "small" awareness or a "big" one. To explain that, while you're doing walking meditation, you can focus right down on your feet. Fine, you can zoom in, that can be a very narrow, focused mindfulness. If you're going to walk to town, don't do it that way! Keep your awareness more open, i.e. listen for cars, motorcycles; watch out for dogs; even a snake might jump up onto the road from the ditches there. So, we need a broader Awareness, broader Mindfulness. There is that difference: we can narrow in, and we can expand it out.
There's also another difference between "mindfulness" and "Mindfulness", and that is in the sense of knowing just what you're doing right now. I am raising my arm and moving it over to the right. If I was just aware of my arm moving - my arm going over - that's a "small mindfulness" - just being aware of the physical movement. But, if somebody is sitting right next to me, I just hit them in the face! So that's not a "big Mindfulness", that's not "big Awareness". So there is that difference also: mindfulness could be knowing what you're doing right now, and that's all; or Mindfulness can be knowing what you're doing now, and the results of what's going to happen from what you're doing. That's a bigger Mindfulness.