It's very simple, "god-given rights" is replaced with "natural rights." It's the concept that rights aren't given by God, but that we, simply by virtue of being human, have certain rights that can't be taken away. Natural rights are derived from natural law, which in general encompasses both the concept of "god-given rights" and "natural rights."
Much as you say one can easily interchange them, Big Ogg with the club wants to remind you about the law of the jungle part of "natural rights".
It's the concept that rights aren't given by God, but that we, simply by virtue of being human, have certain rights that can't be taken away.
By virtue of being human? Why? Big Ogg needs to feed his hungry pet lion & you run slower than the deer. Even you can see the logic in feeding a hungry lion so it won't starve. What gives your life greater value than the life of Ogg's pet lion?
Natural rights are derived from natural law, which in general encompasses both the concept of "god-given rights" and "natural rights."
If you wanna be more than lion food, ya gotta give me more than "natural law".