You can be forgiven for getting lost in the complex names and letters of Nikon products. But one thing is easy enough to remember: Nikon lenses are all branded Nikkor, the name of the company's lens subsidiary. These lenses come in all kinds of shapes and sizes and have a huge range of uses, but anything labeled "Nikkon" was made by and is supported by Nikon.
Nikon's lens subsidiary is called Nikkor. The Japanese camera giant doesn't make a single lens branded "Nikon," but private sellers on sites like eBay and Amazon might call a lens "Nikon" to assure buyers that the lens is compatible with a Nikon digital single-lens reflex camera (DSLR). Every lens that Nikon has ever made is branded with the "Nikkor" tag, though, so when you buy a Nikkor lens you are buying a Nikon product, and vice-versa: buying a Nikon lens means you buy a Nikkor. Some older lenses say both "Nikon" and "Nikkor" on the front of the lens, and a lot of newer Nikkor lenses say Nikon only on the side and Nikkor on the front.
Confusion arises when talking about compatibility between certain Nikkor lenses and Nikon cameras. As a general rule you can mount most Nikkor lenses on a Nikon camera from any era. Yet, even though the same company makes both, not all Nikkor lenses are compatible with all Nikon cameras. Older models from the 1950s through the 1970s are most likely to be incompatible. You may have to use an adapter to get an older lens connected to your brand-new DSLR. When selling these older lenses, however, Web sites try to reassure buyers by calling the lenses "Nikon" lenses when the lenses are, in fact, Nikkor lenses.
Nikon has made a huge variety of Nikkor lenses for the Nikon F-mount system, which is the standard on every Nikon camera made since the 1950s. These lenses go by different names as indicated by the letters after "Nikkor" in the lens name: AI, AF, AF-S, G, VR and so on. All of these lenses are Nikkor lenses and designed for Nikon cameras.
To make things even more confusing, a variety of third-party lens manufacturers – Sigma and Tamron most notably – make lenses for Nikon, Canon and Sony DSLR systems. Third-party lenses end up on eBay with "Nikon" branding, but are not made by Nikon – only for Nikon. These aren't Nikkor lenses, but will work with the Nikon F-mount.
Fraud and perhaps innocently misleading description exist in the world of online shopping. Some eBay (and other online marketplaces) shops purport to sell Nikon products. These shops may even have pictures of "Nikon" lenses or will list lenses as being Nikon-compatible. It's always a good idea to e-mail the shop owner or to send a private message clarifying the lens-mount type. Lenses that are suspiciously low-priced should raise some red flags.