Do the lenses that fit a Nikon D-100 also fit a Nikon D-90 camera body?
Yes. Do not think about them as D100 lenses. They are Nikon F-Mount lenses.
The D100 is Nikon DSLR with a 1.5X sensor crop and will work with any F-mount lens. This includes the Nikkor, Sigma, Tokina, Tamron, etc. Additionally, the D90 and D100 have a built-in focus motor, so autofocus works with AF and AF-S lenses.
It will work with any F-mount lens from the 1980s on. Many of the first Nikkor F-mount lenses have a tang to connect to the old-style meters. This tang will have interference issues with many modern bodies.
I happen to have a half dozen or more pre-AI Nikkor lenses that won't mount of many modern Nikon bodies.