Domestics are raised by people, and depend upon them for food, shelter, safety, water, all those things that people who care for animals do for them. They are bred by hatcheries and I believe they are marked as domestic, since wild mallards are (if I remember correctly) protected under a migratory bird law and only those with permits are allowed to keep them. People like wildlife rehabilitators are allowed to have them if they are injured, for example.
Wild mallards, though they look like the domestics, have not been handled and cared for by people, so they are much better at surviving without the help of people.