If you had asked us the difference between natural and organic, before we had conducted any research on cosmetics and the ingredients they include, we would have said there is no difference. Well that was wrong. Natural and organic are not interchangeable at all.
An article from www.accidentalhedonist.com explains the differences:
A product containing no artificial ingredient or added color and is only minimally processed (a process which does not fundamentally alter the raw product) may be labeled “natural”. The label must explain the use of the term natural (such as – no added colorings or artificial ingredients; minimally processed.) Hormones and antibiotics can be natural. It's the particulars that count.
"Organics" have well defined particulars, "Natural" does not. There are several items listed that organic standards require. There are no such requirements for the "natural" label. To say that there's no difference between "Natural" and "Organic" standards is the same as saying that there's no difference between a Hershey Bar and chocolate made from a Chocolatier in Paris. While both are chocolate, one has more explicit standards than the other.