A natural key vs. a meaningful key, eh?
In this discussion, don't assume that either key has to be "prime" to be involved here.
"Natural" keys are keys that sort of "leap out" at you as "Of course that's a good key." For instance, the Library of Congress book number is a PERFECTLY natural key if you run a bookstore that only carries books registered in the Library of Congress. But it has no particular meaning unless you look up the book in your database.
The Dewey Decimal System for libraries also would be a natural providing you could keep the numbers consistent. In this case, the key would also have meaning because the numbers of the Dewey system convey categories. So the Dewey system would be both "natural" AND "meaningful" for a book key.
"Meaningful" keys are keys that when you look at them, you know immediately what they mean. One could imagine a key of astronomical information based on a body's formal designator. So we would recognize Rigel, Arcturus, Bootes, Betelgeuse, Sirius, Antares, etc. Astronomers would recognize Tau Ceti, Alpha Centauri, Beta Orionis, Gamma Draconis, etc.
Yeah, I know, long names aren't always good keys for efficiency reasons - but they would be good examples of MEANINGFUL keys.