True food allergies are a severe IgE reaction that leads to a Type 1 hypersensitivity. The responses to this type of reaction usually occurs in a few minutes to possibly 4-6 hours after exposure (most responses occur a few minutes to an hour after exposure). It is a severe allergic response that usually grows in intensity with each exposure. It leads to respiratory problems, rash or hives all over the skin, and histamine response. Can cause anaphylactic shock. The most common types of food allergens for this type are peanuts, gluten, soy, and corn.
Food sensitivities or intolerances are also an immune response but a very different immune response. These are sometimes called food allergies too, but they are a response of IgG. The response is delayed and can happen a few hours to 72 hours after the exposure. They are chronic and lead to constant inflammation because usually the food is left in the diet because it is hard to decipher the specific foods. Elimination diets can help to decipher the foods because you eliminate the major food intolerances (gluten, dairy, rice, corn, soy, citrus foods, sugar, artificial sweeteners) and then you put them back in after at least two weeks off of them. It is important wait 72 hours to incorporate new foods because these are delayed responses.
Celiac is caused by having antibodies against the gluten protein. These people have to avoid gluten because gluten causes severe responses in their gastrointestinal tract.
Eosinophilic esophagitis and eosinophilic gastroenteritis are also two food reactions that are non-IgE responses but cause someone to have to avoid foods so they do not have severe immune responses.