An FX (full frame) lens can be used on both a full frame camera such as a Nikon D3 and a DX camera with a crop sensor such as Nikon D300s but the focal length will be different.
A 50mm lens on the D3 will give you the same angle of view as it would have on a 35mm film camera, but put it on the D300s with a 1.5x crop and it effectively becomes 75mm (50 x 1.5)
DX lenses were designed for the smaller sensor. If you put a DX lens on the D3 it only uses the middle part of the sensor, giving you a smaller file and defeats the object of having full-frame.
If using a D300s or similar crop sensor camera you need to multiply the focal length of the lens by 1.5 (1.6 on some Canon's I believe) to calculate what the effective focal length is.
There are other subtle differences too, but that is the fundementals!