For some real facts, let's turn to a good summary article I found on MedicalNewsToday.com.
IgE-Mediated Food Allergies
The parts of the immune system responsible for immediate on-set reactions (the most dramatic example of which is food anaphylaxis) are IgE antibodies.
In allergic individuals (who are sometimes referred to as being "atopic") eating certain food proteins (such as whey and casein protein contained in cow's milk) results in the production of specific IgE antibody molecules directed against the protein. The second time the individual eats the food, these specific IgE molecules interact with each other, and the protein, to cause the release of harmful chemicals (such as histamine) from special mast cells. This causes the damage associated with the symptoms of food allergy. Damage may occur to the skin, respiratory system or gastrointestinal tract, where the symptoms of food allergy are almost exclusively seen.
Non-IgE-Mediated Food Allergy
"T-cells" are the components of the immune systems responsible for delayed-type food allergic reactions. In individuals with a predisposition for delayed on-set food allergy, initial ingestion of food protein leads to the production of specific types of "T-cell". When the food is subsequently ingested, the food protein is "processed" in a variety of ways and "presented" to the previously generated food-specific T-cells. These T-cells then "invade" the area of the body about to suffer damage, as the skin or the bowel. This processing, presenting and invasion can take 24-48 hours which explains the delayed response. T-cells release chemicals that, through a chain of events, lead to the damage associated with symptoms of food allergy.
IgE mediated reactions are sometimes referred to as "true" allergies, while non-IgE mediated reactions are sometimes called hypersensitivities. Unfortunately, these names are not consistently applied inside the medical profession or by the press.
You should also check out the entry on my website, Lactose Intolerance versus Milk Allergy, for a quick reference chart of the differences.