Yep, Phillip is right: A 200mm lens is a 200mm lens whether it is on a DX body or FX body. The lens properties (focal length; aperture) do not change just because you mount it on a different camera.
To explain things completely you have to think about the fact that the DX sensor is physically smaller than an FX sensor - about 2/3 the length and width. So, if you consider the image you can see with a given lens on an FX camera, that same lens will give a more narrow angle of view on a DX camera because of the smaller sensor. The image you see and capture with a DX camera is like cropping down to the central 2/3 of the FX image. With Nikon the difference between DX and FX can be expressed as DX is about 2/3 the size of FX, or FX is about 1.5 times the size of DX. As a result of this if you put a 50mm lens on a DX camera and a 75mm lens on an FX camera they will both have (approx.) the same angle of view and the images in the viewfinders will look essentially the same. Alternatively, if you put a 50mm lens on each camera, from the same position the DX camera will provide a more narrow angle of view than the FX camera. This is what has led to the use of the common term "crop factor" when referring to DX view as compared to FX view with the same lens.
All lenses create an image circle projected from the rear element onto the sensor and, for most uses, the sensor must fit within this circle. If you are designing a DX lens it does not have to cover as large an area as a lens for FX. As a result, one of the advantages of DX lenses is that since they do not have to cover a sensor as large they can (usually) be made somewhat smaller and lighter than a comparable FX lens. One of the disadvantages, however, is that if you mount a DX lens on an FX camera (and stay in FX mode) the lens probably won't cover the entire FX sensor, resulting in very dark corners.
So, you will often see references to DX lenses being the "equivalent" of a 1.5x longer lens. This is really only useful if you are already familiar with what angle of view would result from a given lens on a 35mm film camera or FX camera. If you are not familiar with what the view through a particular focal length will look like on 35mm/FX then the comparison, or mention of the "crop factor," will be pretty useless. In fact, for most cases the best thing you can do is to ignore the "crop factor" and just realize that a "normal" focal length lens on a DX camera is around 30mm, and anything longer than that becomes a telephoto and anything shorter becomes a wide angle (and the farther the focal length is from 30mm the more telephoto or the more wide angle the lens).