It seems that many want to be under the umbrella of Atheism but do not agree on its definition. Atheism is affirming the nonexistence of deity.
There is an umbrella. Google atheism and you get a box defining it as:
disbelief or lack of belief in the existence of God or gods.
Atheism incorporates both ways of thinking. An atheist may make a positive statement about the non existence of a deity. Personally, I will say that I have a lack of belief in a God in the absence of any evidence. It is a rational approach to demand evidence to be provided before accepting something as true. It is up to the believer to produce that evidence before assuming that thing's existence.
My position is that it is more technically accurate to state a lack of belief in God. Just like it is more technically correct to say, I have a lack of belief in Santa Claus. But I have no issue really with saying Santa Claus doesn't exist because without any evidence why should I even consider it?