I have heard the terms "law of nature" and "law of physics" used interchangeably, but is there any difference between them?
Law of nature, in the philosophy of science, a stated regularity in the relations or order of phenomena in the world that holds, under a stipulated set of conditions, either universally or in a stated proportion of instances.
So the Britannica
This is very abstract but it does cover all the "laws of physics" which are things like Newton's three laws of motion. Basically, a law of physics is a law of nature of the sort that a physicist would study. This is a large subset of the laws of nature and so gives many situations where they would be interchangeable.
Some are not. We still refer to Mendel's laws, but we would call them "laws of genetics" or possibly "laws of biology" even though they are laws of nature.
The question amounts to asking whether every phenomenon of nature falls under the jurisdiction of physics.
(1) Saying yes implies ( or seems to imply) a reductionist stance: one could argue that physical laws, though basic and fundamental, do not account for all sorts of natural phenomena ( for example biological phenomena).
(2) Traditionally ( since Kant) nature( realm of all phenomena) is divided into spatially extended nature ( studied by physics) and psychological phenomena ( taking place in time , but not in space). So, if there are actually psychological laws, these are natural laws, but not physical laws.
Reference : Kant, Critique of pure reason ( Theory of method).