[Chemistry] What's the different between "natural" and "artificial"/"synthetic" chemicals?

Seeing labels like "all natural" thrown around by people that don't know an organic molecule from a flux capacitor always elicits eyerolls in me. Non-scientists seem easily convinced by superficially-plausible-sounding statements like "X is natural and Y is artificial, therefor X is better", which is an obvious non sequitur (i.e., ricin is quite naturally occurring, but consuming aspartame is probably a better idea.)

Clearly "artificial" chemical compounds aren't created via alchemy or magic. They always start with some "natural" materials, undergo some kind of process of physical reactions governed by "natural" laws, and end up with some kind of product. Whether or not humans were in the production loop, the same processes occurring in nature would lead to the same result.

Chemists/materials/bio people, how do you draw the line between "natural" and "synthetic" materials? Is such a distinction ever actually meaningful?