While it is not the end of the world if we do not use words about philosophy exactly as someone else does, these two words have some importance in arguments about religion. I am guilty of not using the words precisely.
One of the funniest things Newt Gingrich said during his bungled campaign for the Presidency was his grandchildren may have to live in a secular, atheist country dominated by Isalam. How any country could be secular, atheist and Islamic at the same time is beyond me.
Technically, secularism has nothing to do with people either being religious and being not religious. It is about a government that is not religious. Thus, the very successful organization, Americans for the Separation of Church and State, is headed by a minister. As I recall, it was founded by people who belonged to churches, not atheists.
It seems to be in the interests of some clergy and politicians like Gingrich to confuse people about the definition of secularism. They do this by mixing it together with atheism, and, even the religion of Islam.
Some atheists mix them together also. There are unbelievers who do not want religion to be available to anyone. If this were the case, they say, we would have a secular country. It would be more accurate to call it an atheist country, hopefully with a secular government.
Thus, a secular country could be dominated by either religious or not religious people. The founding fathers seemed to have this in mind.