How do milk allergies differ from lactose intolerance?

Antibodies: People with a milk allergy develop antibodies to proteins in milk; every time they are exposed to those proteins (whether it's a little or a lot), they have a reaction. People with lactose intolerance are missing an enzyme that allows them to break down lactose; without the enzyme, the sugar in milk passes through their digestive tract unchanged causing symptoms. A little milk is often tolerated.

Food Allergies: Milk allergy means you have an immune-mediated (ige) allergic reaction to the dairy proteins whereas lactose intolerance is simply the lack of the lactase enzyme which is used to break down lactose, the primary sugar in milk.