This is just my opinion on this but I think clean beauty products are eco-friendly, sustainable, cruelty-free, free of toxic/harmful ingredients but the ingredients can be natural and/or synthetic. Natural ingredients (or organic ingredients which really should be certified) contain raw or “”pure”” ingredients derived from nature, usually plant-derived.
IMHO clean beauty is a marketing term from the 1970s. CoverGirl was the first to really refer to their cosmetics as clean back then. Then it was taken up by Ren, which means “”clean”” in Swedish. Nowadays, some brands are notorious for spinning clean beauty like Drunk Elephant, but it is always in a fearmongering manner, which can work on uneducated consumers (and frankly most of us are). The Think Dirty app also works in a similar manner, providing a hazard score for cosmetics but I think that sort of thing is only marginally helpful. Clean beauty and brands which promote them really contribute to a major disconnect with scientific facts.
tl;dr “”Clean beauty”” does not necessarily mean chemical-free, but it claims to be “”natural””. “”Natural beauty”” is free of man-made ingredients (e.g. parabens) and can include clean ingredients.