I guess it has to do with the fact that in the USA, driving licence and state ID card are used not only for driving and identification but for residency proof as well. When you move to a different state, you typically surrender your driving licence or ID card to get a new one from the new state. However, if you have both DL and ID cards, then you can retain one of the previous state's document and still get benefits from there even though you moved out. AFAIK, some states allow to hold both DL and ID (e.g., California).