No matter whether you use an 18mm FX zoom or an 18mm DX zoom, you will get the same field of view when those lenses are mounted on a DX body.
When an 18mm DX zoom is mounted on FX, and IF the FX body is set to automatically identify a DX lens, the image you see through the viewfinder should look like it normally would for an FX body (remember, there isn't any crop factor visible when viewing through an FX viewfinder). BUT the size of the file will be smaller from the FX body because part of the image you saw through the viewfinder is cropped away in camera--and the image you see afterwards will be the cropped image.
If the FX body isn't set to automatically sense there is a DX lens mounted, then you will get a full resolution file that usually has vignetting and loss of quality at the corners. Those areas that have the loss of quality and vignetting are the areas that would normally be cropped away IF the FX body was set to automatically sense a DX lens. So what you'd need to do in those circumstances is to crop the image yourself. And you still wind up with a smaller sized file.
Just remember that the field of view is different when looking through a DX body vs. FX even when the FX body is set for a DX lens. DX bodies have the 1.5 crop factor applied to the viewfinder. On an FX body, you will only see the FX field of view, not the cropped DX view no matter how the body is set.
Clear as mud, I'm sure.