Answer:
A Bain Marie is a water bath with another section for the food to be cooked to be placed. The water is heated, and the food is placed in the other section then submerged. The heat of the water cooks the food.
A Microwave Oven uses radiation energy to heat the water molecules within the food, which in turn heats the food.
So to answer, the method by which they cook food is different :)
Sources: personal experience, and links in related links