Atheist versus non-theist. For me they are different. I feel Atheist is more antitheism where non-theist is "I just don't care". I feel I am more non-theist. I don't often consider religion at all, including not believing. It all sort of doesn't exist for me.
There is zero difference between those two words. That's what the prefix "a-" means. Lacking a belief in deities. The appropriate terminology describing anything beyond that exists.
Edit: essentially what I'm saying here is care enough to learn the terminology. Else you risk painting us all with the same brush. Personally, I would never say that the possibility of God is impossible. Strong atheists don't agree with me.