I think they are the same thing. One could learn the rules of chess by reading the manual, learning the game from a friend or simply observing the playing of the game. The rules are the rules.
However, it looks like you've reversed things in your interpretation of the chess analogy. The observing of the playing (observed regularities) are "the derived rules" and the chess manual (our models) are "the given rules".
We see certain things happening in the real world, and there are real world causes for why those things are happening, and when we look closely, we see that some of those real world happenings are repeating with regularity, and there is an underlying real world cause for those regularly repeating real world happenings. It is my belief that the term, "laws of nature" refers to those real world causes that serve as the foundation for the repeated regularities that man has come to observe.
So, before man enters the scene and starts observing the effects of the laws of nature, there are already laws of nature giving rise to the unobserved regularities. Once man sits up and takes notice, he sees not the laws of nature but rather the consequences of their existence--the regularities that become observed.
It's only after we have observed the effects of the laws of nature that we begin to study and finally write down our formulations that help us explain the cause for why we observe what we do. When we ordinarily speak of laws, we speak of that which we, man, has formulated and written, but such is not the case with with the laws of nature. That is not a law born of man subsequent to observations but rather a 'law OF nature' born before our own existence.