Food Hypersensitivity is an umbrella term used to describe adverse reactions to foods, including wheat.
Food hypersensitivity includes Food Allergy (IgE and non-IgE mediated) and food intolerance. Wheat allergy involves the immune system, whereas wheat intolerance does not. The mechanisms of wheat allergy can be divided into IgE mediated wheat allergy (characterized by reactions occurring within minutes to 2 hours of eating or inhaling the allergen) and non-IgE mediated wheat allergy (characterized by reactions occurring between 2-48 hours of longer) [1].
Reference
Johansson SG, Bieber T, Dahl R, et al. Revised nomenclature for allergy for global use: Report of the Nomenclature Review Committee of the World Allergy Organization, October 2003. J Allergy Clin Immunol 2004 May;113(5):832-6.