The difference is that between two immune related reactions, allergy and intolerance. I asked the question of the technical difference between the two some time ago and got no response. Its not based on overt symptoms, thats for sure. Were also not talking about the difference between latent celiac disease and overt weight-loss, apple belly celiac disease. You can be allergic and intolerant of the same substance or food In the case of milk, its lactose(milk carbohydrate) intolerance and milk protein allergy.
My non-professional stab at the difference between intolerance and allergy then. Both can lead to intestinal damage. Theres a table in Marshs book showing that --page 155 , figure 6.13. Type 3 damage (flat destructive ) can occur from milk, soy, egg.... as well as celiac disease.
The reaction to an intolerance seems to be that the substance is not digested. The immune part of the response involves only the circulating immunoglobins IgA, maybe IgG and related immune cells, receptors.
The immune reaction to an allergy involves IgE. The substance may still be digested, but there may be allergic responses elsewhere outside the gut.
Apple belly celiac disease is an intolerance. The problems elsewhere in the body, except for cancer, are related to nutritional deficiencies. The link to other autoimmune diseases is statistical genetics when two (or more) genes for each of two conditions are close together.
For more information see the Allergy vs. Intolerance page.