I knew a family during my childhood that claimed to be ‘Atheists’, yet the mother said that she believed there may be a higher power at work sometimes, but didn’t acknowledge that it was GOD. I guess she wasn’t a traditional Atheist.

People are not born atheists or believers. They become one or the other, usually believer first in this age. When one, through personal growth or life experience or what not becomes atheistic they can become plagued by certain schisms because the early conditioning is very strong. Not to say that one can’t go from atheist to believer and have the same problem. Anyway the atheist bound person may revert to praying and such intermittently or just decide that they can handle both praying or believing on occasion, this would be an intentionally schismatic individual. Eventually they decide the praying part is simply talking to themselves and they drop it, almost completely or completely. Old habits die hard. Agnosticism and deism are different and etiher may apply to the woman in question. I guess I would call my self agnostic but I don’t believe attaching a religious label to myself is really very important. The fact that other people do is a big topic of interest.
Sorry to anyone who already knew this stuff.