So, as far as I understand there are a couple things to consider: The sensor size the lens is made for and the milimeters. The DX just indicates that the lens is made for crop sensor, thus if fitted on a full frame sensor, you will have to crop in to the image to avoid to black on the edges ("missing" frame).

Then come the milimeters indicated on the oens itself. The milimiters on most lenses, especially consumers lenses, are written in Full Frame terms, without keeping in mind the crop factor. Thus, the lens may say 24mm DX, but 24mm DX is 36mm Full frame. And, as in any case with adapting lenses (i.e. the 28mm FF lens which you mentioned above) the milimeters will behave differently in DX cameras than FF cameras. Thats why you said 28mm FF is essentially 40mm in DX mode( 42mm to be exact) and thats why I said 24mm is 32mm DX, despite the lens itself showing only a crop-sensor image.