@fBoyle-- That's a great question. I think mineral, organic and natural lip gloss can be the same. You have to check the ingredients of different products to see what they are. Mineral lip gloss contains only natural ingredients and avoids chemicals and synthetic ingredients.
Organic is something different though. Something can be natural or mineral but not organic. Products that claim to be organic have to be approved by the FDA. That's why you see "certified organic" on the label of those products.
Mineral and natural seem to be the same but I personally think that "mineral" implies "mild." I have friends with sensitive skin or skin problems like rosacea, who can only use mineral products because those don't irritate their skin. "Natural" is a claim that can be made by any product and it doesn't mean a lot. A product can contain both natural and synthetic ingredients and be labeled "natural."
If you want mineral lip gloss, ignore the product claims and check the ingredients list. A lip gloss that only contains natural ingredients like natural oils, beeswax, etc. is a mineral lip gloss.