Surely they are the same thing?
Depends on how they are defined.
In my mind I was thinking of the laws of nature being more associated with the living world, in others words planet earth, which might not reasonably apply to, say a black hole. The laws of physics are more fundamental and universal covering everything - so you might say that a black hole complies with the laws of physics, but the laws of nature aren't really relevant. However evolutionary processes comply with the laws of nature, which are themselves based on the fundamental laws of physics.
In effect the notion that biology is a specialised branch of chemistry covering living things - which chemistry being a specialised branch of physics covering matter. Physics, and its laws being the most fundamental covering everything.
But I guess it depends on definitions.