This is partly a definition question, and partly a political one. Basically, an atheist is someone who believes there is no god, while a secularist is someone who doesn’t believe there is a god. (That’s not the same as an agnostic, which just isn’t sure either way.)
I feel the need to make this distinction because the term “atheist” has been used by defenders of religion to argue that atheism is itself a religion–that is, the absence of belief, or the refusal to believe, is itself a belief. The political purpose in doing so was so that fundamentalists could challenge the teaching of evolution in public schools on the grounds that it was establishing religion–the “religion” of atheism. (Alternatively, “secular humanism,” but I’ll come back to that.)
In earlier times, I think this conflation would have been unjustified, but now that we see militant atheists who attack religious believers (sometimes literally, as in Stalinist Russia), and who want to denounce all religion and remove it from public life.
In response to this militancy, both on the part of some atheists and of their opponents, many people who no longer believe in a god began to define themselves as secularists. I understand “secularism” to mean a lack of belief of a god, but also a lack of militancy about it. Secularists are not (or not as much) bothered by the religious, even the fervently religious, as long as they don’t try to seduce, persuade, or most especially force the non-believers to believe, or try to demand that the general public subsidize their belief.
On a broader scale, we can and do refer to countries like the United States as secular countries, since while many of its people are religious, there is no established religion, no one is required to believe, and (ideally) religions are not subsidized. (OK, the US slips up on that last one.)
So the fervently religious have tried to blame “secular humanism” or “hedonistic secularists” for the ills of society, for Hitler, Stalin, and Mao, attempting to tar “secularism” as being “atheism” under another name. My impression is that this hasn’t worked, though they are still trying.
This comes to mind right now because I am still grappling with the consequences of religion on war. It has long been clear that religion is often a factor, though not the only factor, in war, but I also have to acknowledge that there has warfare against religion as well on its behalf. So I think the point of commonality is ideology, and more importantly, purity of ideology. Catholics and Protestants fought a hundred years of bloody war because each was convinced that the other side’s beliefs were going to doom them to hell, and they didn’t want to be contaminated by those impure beliefs. Wahhabism started as a reaction to those forms of Islam (Sufism, especially) that the Wahhabists thought were too lax, that is, not sufficiently pure. Followers of Meir Kahane want all Arabs driven out of the “Holy Land” because their presence contaminates the purity of Judaism; Haredi and Hasid fight over whose recreation of a middle European ghetto is more pure. Marxist atheists thought the Orthodox church was getting in the way of the creation of a pure communist society.
Yes, this is something of a caricature; this is a short essay and if you want the more nuanced version, you’ll have to wait until the book is out. The point for the moment is that here is where I see secularism, as I define it, as a path to earthly salvation, if you will: Secularism requires pluralism and therefore doesn’t care about purity.
Anyway, that’s where I’m hoping the chapter on war will lead me to. So far, it’s working.