Correct, I believe the first is about God, as stated. God given right of all human, in the pursuit of happiness, derived from the Bible. The Christian faith, which is the reason for empowerment of the revolutions against the crown, and other defects that ails the second nation, USA , such as the slavery, women's rights and other protection built-in for other minority groups.
That fact is still what makes the separation of church and state possible, etc. It should be celebrated & defended, by all freedom loving people.