The exemption, and its two conditions
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The rule is two sentences long and almost nobody in the craft has read the second one.
Both conditions, not either
21 CFR 701.20 sets out when FDA treats an article as "soap", and the two conditions are cumulative.
Fail either and the product is not exempt soap.
The composition condition
The bulk of the non-volatile matter in the product must consist of an alkali salt of fatty acids, and the detergent properties of the article must be due to those alkali-fatty acid compounds.
Which is a chemical description of real soap: fats or oils reacted with an alkali.
The consequence is that a bar whose cleansing comes from synthetic detergents is not soap for this purpose, whatever the package says. And a bar containing a substantial proportion of something else may fail the "bulk of the non-volatile matter" test.
The representation condition
The product must be labeled, sold and represented only as soap.
Three verbs, and all three have to hold. Not only the label: how it is sold and how it is represented, which reaches the website, the market sign, the listing category and what you say to a customer.
This is the condition that fails, and it fails on a word.
Why both matter
A maker who reads only the first condition concludes that because their bar is genuinely saponified oils, it is exempt soap.
It is not, if the label says moisturizing. The composition condition was met and the representation condition was not, and both were required.
Which makes this the cheapest compliance decision in the estate to get right and one of often got wrong.