1. Disbelief in, or denial of, the existence of God or gods.
2. The doctrine that there is no God or gods.
1. The view that religious considerations should be excluded from civil affairs or public education.
2. The doctrine that morality should be based solely on regard to the well-being of mankind in the present life, to the exclusion of all considerations drawn from belief in God or in a future state.
1. A system of thought that rejects religious beliefs and centres on humans and their values, capacities and worth.
Hence one can be a secularist without being an atheist, although the reverse is I suspect rather difficult. While atheists are generally secularists, at least in Europe so are most believers because they know their own freedom of belief depends on freedom from the belief of others. Humanists are by definition atheists.
Atheism challenges belief but secularism challenges religious privilege. Humanism replaces a belief in god(s) with a belief in Homo sapiens.
And yes, for the record I am both an atheist and a secularist. I'm also a humanist but not one who identifies with humanism as an organised belief system, a là British Humanist Association — I don't do organised belief systems!