Nikon for the cameras, unless you include some very ancient and long forgotten models (Nikkorex) not even made by Nikon themselves, and of course the lower-end-of-range Nikkormats of the '60s.
The Series E lenses introduced for the Nikon EM in early '80s comprise the only internationally available lens range carrying the Nikon designation, commonly known as Nikon SE lenses.
Thus with very few exceptions, lenses for the Nikons are designated Nikkor. There is no option in the nomenclature so a lens either is a Nikkor or (rarely) a Nikon, but one cannot use these labels interchangeably.
'Nikkor' and 'Nikon' are all encompassed by the Nikon brand as such. Nikon gear is made in a number of Nikon factories in Asian countries (China, Thailand, Indonesia) besides what is made in Japan proper.