To me the question strikes at the heart of the modern debate about natural and artificial kinds. The term "natural kind" was introduced by Mill and then forgotten until Kripke and Putnam resuscitated it in 1970s, but the idea goes back to Plato and Aristotle. Namely, that things out there fall into "natural" categories, which science discovers by, as Plato expressively put it in Phaedrus, "carving nature at its joints". Those are also known as the "essential" properties, and the view itself as scientific essentialism.
The identification of natural kinds is tangled with modal metaphysics a la Kripke and, his also with Putnam, causal theory of reference. This is where the rigid designation and "water is H2O", as a necessary a posteriori, come from, see What is the relationship between Kripke's rigid designators and scientific realism? The Kripke-Putnam theory depends on a strong notion of "modal intuitions" which dictate that in other possible worlds the identification of the molecular structure of water might have gone differently, but the end result remains rigid, hence the necessity. So by analogy, it matters not that synthetic elements can only be produced artificially, once they are what they are is an a posteriori necessity, hence "natural". On the other hand, there is no necessity in Leonardo painting Mona Lisa as opposed to somebody else, or painting her exactly as he actually did, or there being a Leonardo for that matter, or Coca Cola being the particular drink we know (and love?).
Modal metaphysics, necessary a posteriori, and scientific essentialism with natural kinds are controversial. How do we know what is or is not rigid? "Consult your metaphysical intuitions", as Almog put it in Naming without Necessity. Dupré in Natural Kinds and Biological Taxa shows how the modal strategy falls apart for biological species:"I will assume the interpretation of biological taxonomy most favorable to Putnam's theory, and show that even this is often not as Putnam needs it to be." Ben-Yami in Semantics of Kind Terms gives a more broad recent critique of natural kinds, and concludes that "there isn’t any difference between natural kind terms and other kind terms in their semantic function, in the way their reference is determined, or in the way they are introduced into language."
In practice, what essentialists seem to have in mind as "natural" are aspects of objects (more precisely, of universals) that are particularly closely tied to what we consider the laws of nature. Given the contextuality and fallibility of our knowledge about the latter, presumably our identification of natural kinds is equally contextual and fallible. Hacking's Tradition of Natural Kinds offers a pragmatic view that may accomodate such use without "Plato's unsavoury rubbish about carving nature at the joints":
"We can devise rough and ready characterizations of 'natural kind'; none are precise, but with good will and a little charity we can agree, in most cases, on what is a natural kind according to a given characterization... For various purposes and interests there are better and worse, more fruitful and less fruitful classifications of objects, organisms and substances."
This sort of fruits vs vegetables distinction between natural and artificial kinds along a continuum might satisfy even Quine, who was having none of it in Reference and Modality, exactly because he saw metaphysical essentialism as incompatible with (his) scientific naturalism. He was even willing to throw out modal logic along with it:
"An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the object as the former traits do from other ways of specifying it... the way to do quantified modal logic, if at all, is to accept Aristotelian essentialism... Such a philosophy is as unreasonable by my lights as it is by Carnap’s or Lewis’s. And in conclusion I say, as Carnap and Lewis have not: so much the worse for quantified modal logic.
