I would classify a food intolerance as something that gives you digestive issues but is not immune mediated. One of the big reasons for increased food intolerance is the increasing presence of glyphosate in our food supply. Most grains at least in North America are contaminated with it since farmers are using Round-Up as a desiccant and spraying it on the crop just before harvest.

I would add another category to your post however: That of Food Sensitivity.
A food sensitivity is mediated by the immune system and causes increased inflammation throughout the body. They occur from having a chronic leaky gut. It is caused by IgG antibodies becoming activated while allergy is caused by IgE antibodies becoming activated.