Alright, let me start by saying that I am a full blood Atheist.
Now, The wand mirror, you've completely gotten this the wrong way. Being a Satanist have to include Satan in some way or the other, thus not believing in anything religious, and not being very fond of Christianity is not being Satanistc. Its called more or less being Atheistic, or nothing at all.
And, Hakeem, the term Atheistic Satanism is a headline referrance to various smaller sorts of Satanism, such as Symbolic Satanism. The belief still includes Satan, but more like symbol of freedom and self-control. Not as the religious figure known through Christianity and Theistic Satanism, yet all the same it is based on the same thing; Satan.
This also means that your statement about that Atheists and Satanists are more or less the same thing or considering themselves as the same thing isnt right. Shortly spoken, Satanism includes satan, while Atheism does not, any Atheist believing in Satan is no longer an Atheist, thus again, not right at all. And no, I cant see it that way.
In the end Satanism and Atheism is two different things, yet I wont say VASTLY different as Satanism is a very covering word, including various beliefs, which is; Symbolic Satanism, Theistic Satanism, Temple of Set and LeVeyan Satanism. Which all are different in each of their ways, yet at the same time includes the very figure of Satan in some way or the other. Yet I can see how people tend to believe that their more or less the same thing.