I was wondering if atheists, or anyone in general can tell me why so many people confuse these two. I don't have a problem with atheists or atheism, but why do so many atheists claim, "there's no discernible proof of God, so we can't know for sure?" I'm not disputing the validity of such a claim, but that isn't an atheist claim.
Well they mean they same thing really. Just like muse means to think and amuse means to not think. Prefix 'a' is a sort of "non" "not" "negative" "opposite"
I have never heard of non-theist being used. Atheism in its simplest form is the lack of belief in gods, or the rejection of the claim that at least one god exists. Agnosticism is the position that the existence of a god or gods is unknown or unknowable. Many atheists also fit into this category. The reason they claim there's no discernible proof is really because there isn't.
The actual definition of atheism is simply the lack if belief in ANY gods. You are confusing atheists with agnostics. Agnostics are the ones who allow for the possibility of God's since they don't know for sure.