(I posted a longer version of this on my website: https://aftergod.net/2019/06/25/atheism-or-secularism/.)
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 and then used this argument to make political attacks on atheists.
In earlier times, I think this conflation would have been unjustified, but now 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.
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, ideology in pursuit of purity. This 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.
That's my working definition and hypothesis, which is becoming a theory. Your thoughts are welcome.