I see those as essentially one and the same. Especially if they are reduced to assumptions. And I'm not sure what else they can be unless someone can establish what God is. But that leads to man defining God. But without knowing what God is the question of (non)belief seems meaningless. What is it you are (non)belieiving in? --It is based on this agnostic view that I chose to not believe, which I hold to be something different from (non)belief.the most fundamental of all assumptions is a belief or nonbelief in God
Further, if we cannot know God, in a way to at least communicate what you know as justified true belief, that we cannot know what God considers right and wrong. All we have to go on is what we do know of our nature as reasoning, social beings. What is right is that set of actions that enable us to be who we are, according to our nature, to achieve some dignity and happiness, and what is wrong is what interferes with that.
I will add that if you choose to believe then that is good for you and I respect that as part of the liberty of conscience we all share as long as we are free to.
That said I contend that the position taken in this thread seems to be derived from Augustine while mine is derived from Aquinas. Quoting from Rothbard's The Ethics of Liberty:
Rothbard goes on to explain this Thomistic position with reference to the Spanish Scholastic Suarez:
Natural law is true regardless the existence of God as its Creator.