Me
The combat chapter of the PHB has the following to say: "Effects that modify weapon damage apply to the unarmed strikes and the natural physical attacks of creatures" p134
Glass
Again, indicating that unarmed strikes and natural weapons are separate things.
No. It does not eliminate the possibility that the drafter of that section considered unarmed strikes to be a kind of natural weapon.
For example, when a lawyer drafts a document that refers to "natural heirs, children, decendants, and..." he isn't saying that those are seperate things. "Children" are a subset of "Descendants" (which can include grandchildren, etc.) and both are a subset of "natural heirs" which can include many blood relatives (like uncles, parents, grandparents, and cousins) depending on who died when.
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Glass
EDIT: You have also studiously ignored the fact that elves, dwarves, halflings, etc (who all have unarmed strikes) are not listed as having any natural weapons in the MM. How do you reconcile that one?
Me
Besides, the MM entries don't even list the unarmed strike for any of those races, presumably because the unarmed strike is a weapon of last resort for most members of the species.
Glass
No they don't have unarmed strikes, they can use unarmed strikes, just like any other creature that can move.
The MM is, at best, inconsistent.
Traditional (Core) PC races only have weapon attacks listed in their stat blocks. The Centaur only gets use hooves during a full attack.
Among giantkind, Ogres and Ettins (listed INT 6) have only weapon stats, but meanwhile all of the standard Giants (who are smarter & more civilized) have natural attacks AND weapons listed in their stat block.
Djinni & Efreeti (who are depicted with falchions) only have slam attacks listed, but Janni have only weapon attacks listed. Doppelgangers also have only natural attacks listed, even though the description clearly states they use weapons when disguised.
Balors list natural attacks & weapons, but pit fiends do not - though both creature descriptions make note of the use of weapons.
None of them- all presumably "creatures that can move" - has an unarmed strike listed.