The difference is the ability of the government to pass arbitrary laws. There are (currently, in the West) two opposing views: natural law (laws are the refinement of what already is a natural part of human aspirations), and consensus law (law is what social consensus agrees upon). There’s also authoritarian law, but that is dictatorship.
Of these possibilities, only natural law can command respect. Society can be irrational and pass arbitrary laws for longer than you can stay sane, and dictatorship is, well, dictatorship.
The US constitution and the bill of rights are explicitly based on the idea of natural law.
The concept of Natural Law was an important part of enlightenment legal thinking. When the Declaration of Independence invokes the 'Laws of Nature', it's authors would certainly have been aware of and intentionally referencing contemporary thinking on the subject to justify the declaration.
In fact we know from some legal decisions of the time that Natural Law was explicitly used as justification for various legal decisions, in the absence of explicit written laws on the subject.
Of these possibilities, only natural law can command respect. Society can be irrational and pass arbitrary laws for longer than you can stay sane, and dictatorship is, well, dictatorship.
The US constitution and the bill of rights are explicitly based on the idea of natural law.