What the label must carry, in each of the three cases
Updated
A consequential page in this property, because the determination you made earlier decides which of three labels is the legal one.
Three labels for one product
The same bar, unchanged, carries a different label depending on how it is represented.
Which is unusual: in most crafts the label follows the formula. Here the label and the marketing are part of what sets the category.
Get the category first, then this page tells you what goes on the package.
Exempt soap
Outside FDA's cosmetic authority, and a consumer commodity, so the Fair Packaging and Labeling Act requirements apply: a statement of identity, a net quantity of contents, and the name and place of business of the manufacturer, packer or distributor.
No ingredient declaration is required.
And CPSC is the agency with jurisdiction, including the Federal Hazardous Substances Act where a product contains a hazardous substance.
It is the lightest of the three labels, and it is available only if both parts of the exemption hold.
A cosmetic
Everything above, plus an ingredient declaration in descending order of predominance using INCI names, plus any required warning statements.
And under MoCRA, facility registration and product listing obligations, with small business exemptions that have to be read against your own numbers rather than assumed.
This is the label most handmade soap actually needs, because most handmade soap is marketed with at least one cosmetic claim.
A drug
A different label entirely: a Drug Facts panel, an active ingredient statement, and compliance with the applicable monograph or an approved application.
Plus drug facility registration and drug listing, and the manufacturing requirements that go with it.
Which is why the practical advice throughout this property is to avoid the claim rather than to build the label, unless you are deliberately making a drug.