Okay, a soft atheist is someone who doesn't believe in god, because they don't see any proof or evidence for the existence of god. A hard atheist is someone who says that there is no god, because they don't see any proof or evidence for the existence of god. The difference is simple. The soft atheist says"i don't believe your claim, due to the lack of proof". The hard atheist says"there is no god, due to the lack of proof". One is stating a lack of belief. The other is stating a counter-claim, that they now have to prove.
And no, lack of proof for someone who requires proof isn't enough proof. It may be, for that specific person, but using logic, and being rational, means that it isn't good enough. Not to make a claim, anyway.