As dayyw1 says,
downy mildew is a pale white / grey fungus that coats the leaves. It is highly visible.
White rot is not visible as all the action is happening underground. The only indications tend to be a sick looking plant which can often be pulled up without any effort because the roots have rotted. As well as rotting roots the underside of the bulb has usually also started to rot.
White rot is much more serious. Downy mildew can (and often does) happen site-wide while white rot is more likely to be plot specific.