What is the main difference between milk allergy and lactose intollerence?

Indigestion, allergy: Milk allergy is a term reserved for reactions due to allergy sensititivity to milk protein, resulting in immediate reaction including hives, breathing difficulty, vomiting and diarrhea. Lactose intolerance results from poor capacity to digest lactose, a sugar that is present in milk. Poor lactose digestion produce gas in excess, with cramping and diarrhea.