Is a food intolerance an adverse reaction to a food that involves production of antibodies?

Food intolerances: Classically not though some researches believe that igg4 mediated responses fall under this classification. So do non-immunological food reactions such as sucrase, maltase , lactose etc deficiencies.

Not necessarily: Some are, like food allergies or gluten induced celiac disease. Others like lactose intolerance is mechanical.Since you can't digest lactose, it becomes a diarrhea inducing agent. Some food additives like red #40 trigger will trigger diarrhea in some.

Food allergy: Food allergy is an adverse reaction to a food that involves production of antibodies - specifically ige antibodies. Food intolerance is a general term for any reaction to any adverse food other than food poisoning. Food allergy is a form of food intolerance.