If you have a true food allergy, your immune system reacts to the allergen protein in the offending food, resulting in symptoms such as itching, hives or the more severe anaphylaxis. Symptoms usually occur very soon after eating the food. In the highly sensitive, even touching or smelling a food can provoke a reaction.
If you have food intolerance, you have an abnormal physical response to a food or food additive. For instance, if you lack the enzymes needed to break down lactose (milk sugar), you have a lactose intolerance and may develop diarrhea.