The distinction seems to be that awareness is simply a lower level of mental state than consciousness. For example while many conceive of monkeys or dogs as conscious, in that they appear to have "thoughts", it's doubtful that ants or slugs are conscious in that sense. But they may have some sort of mental state, or "awareness", that we would stop short of describing as conscious.
Panpsychists simply make the point that materialists make the assumption that things don't have awareness unless proved otherwise. But why make that assumption? Why not make the opposite assumption: that things have awareness unless it's proved that they don't? You can say that's ridiculous or whatever else. But is there actually any good reason for loading the question in favour of materialism?
In fact panpsychists go further and point out that we only have experience of being aware. We don't know what it's like to be a thing that isn't aware. In fact, can we even be sure that it's possible to exist and be unaware? We have direct evidence that a thing can exist and be aware (because we exist and we are aware). But obviously we could never have direct evidence that it's possible to exist and be unaware. So why assume that most things in the universe are unaware when in fact we can't prove that anything is unaware. On the other hand we can prove that we are aware, and therefore that at least some things are aware. So maybe our assumptions should be loaded in favour of awareness rather than against it.