What is the difference between, for example, a Nikon 50mm DX lens and a Nikon 50 mm FX lens? Both have the same focal length of 50 mm, but why does Nikon produce a DX lens and an FX lens? What is the difference in the lens construction? Is it just the size of the lenses is smaller in DX compared to FX because FX has a larger sensor? Any other differences apart from size, price and weight?
Price, weight and size, but in particular, it seems important that the DX lens projects a smaller image circle, large enough to cover the DX sensor, but it is not designed to fully cover the larger FX sensor. It can vary with zoom in individual lenses, but generally, large areas in the FX frame corners are dark with a DX lens. A reasonable simulation of this is shown at https://photographylife.com/using-nikon-dx-lenses-on-fx-cameras