The line, in one sentence
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The definition
Antiperspirant: a drug product applied topically that reduces the production of perspiration, sweat, at that site. Note that it says reduces the production, which is about the gland rather than about the smell.
What a deodorant does instead
It addresses odor, by masking it, by absorbing it, or by making the skin less hospitable to the bacteria that produce it. None of that reduces sweat production, and none of it is within the monograph.
So two products can look identical
Same format, same jar, same place on a shelf, and sit in different regulatory worlds. That is unusual and it is why this is the first section rather than a footnote in the labeling one.
The claim can move it on its own
A cosmetic deodorant advertised as keeping you dry, or as stopping sweat, has made an antiperspirant claim. The product did not change; the description did, and the description is enough.
And so can the ingredient
Including a monograph active at a meaningful concentration is doing the drug thing whether or not you say so. Classification follows what the product is and what it is represented to do, taken together.
There is no middle category
A product can be both a cosmetic and a drug, which is the usual position for an antiperspirant that also perfumes. What there is not is a halfway classification with lighter obligations.
Decide it before anything else
Formula, testing, artwork and format all depend on this answer. Discovering it after artwork is signed off means rebuilding the label around a Drug Facts panel that was never laid out for.
It is a determination, not a preference
Classification follows what the product is and what it is represented to do, taken together, and neither half is something a business gets to pick. Treating it as a branding decision is the misreading that produces every failure in this property.