Looking at the following page from Nikon, it seems to confirm that all lenses designed for DX have also a DX in the reference:
https://imaging.niko...p/lens/list.htm
DX designed lenses project a smaller circle of light on the sensor (as they are aimed for smaller sensors) than a lens designed for an FX sensor.
Therefore
- FX lenses can be used with DX sized sensors (the light of circle being larger than the sensor). Using FX lenses on DX sensors have additionally the advantage that vignetting is not caused by the lens, as the projected image is so much larger than the sensor.
- DX lenses can be used with FX sized sensors, however the projected image will only cover part (more or less half) of the sensor. Therefore the resulting picture will only use about 45% of the Megapixels (the ones in the center, included in the area where the image is projected) that the sensor provides.