I want to know what is the difference between being allergic to milk and being lactose intollerant?

Severity: Lactose intolerance is a simple lack of an enzyme that breaks down lactose, a sugar in milk. When sugar gets through to the large intestine, the bacteria go nuts and grow rapidly - producing gas, bloating and diarrhea. An allergic reaction to milk proteins can give similar symptoms, but also some that are much more severe - rashes, vomiting, wheezing, and anaphylaxis, which when severe, can kill.