The first isn't atheism, it is agnostic - no religion and not looking for one, but open to it if you can convince them your religion is right (which you can't because they are not interested in the topic)
Atheism is defined as the absence of belief which is essentially what OP said.
The fact that we are open to changing our mind if theoretically presented with strong evidence does not make us agnostic.
You’d probably also accept that sun is made of cheese if presented strong enough evidence but don’t call yourself agnostic about the topic given your current knowledge.
Atheism is the position that God does not exist. An atheist is someone who therefore says “I believe that there is no God.”
It is not a mere lack of belief, as agnostics can be said to lack belief in God as well. People who are simply ignorant of God also lack a proper belief in God, but this is not atheism, only ignorance. They simply have not come to terms with the subject and therefore have no position on the matter. An atheist does, however unsophisticated it may be.
This view that atheism is simply a lack of belief in God is common among the intellectually challenged New Atheist crowd and would have been ridiculous to the much more intellectually substantive atheists of old, like Neitzsche (who, btw, while an atheist, found it a horrifying thing; the other classic atheists could be described as world-weary rather than insipid, parochial, middle class triumphant).
