To an atheist who doesn't believe in a God or afterlife, this belief (or non-belief, however you like to view it) is in one way or another of importance to them. It is important to an atheist that they do not believe in religion.
To an apatheist, it doesn't matter wether or not there is or is no God. Either way the question can't be proven and debate towards this end is futile and pointless. Apatheists are indifferent and are closest to the term 'non-believers'.
Your own stance is almost closer to apatheism than it is to atheism. Although from the fact that you decidedly closeted your beliefs does at least insinuate that the choice of not believing anymore empowers you in some form so you still lean towards the atheism side of that spectrum.