Technically yes, avoidance is the solution for both for most foods. Realistically I would not split that hair, however medical professionals often use the differentiation to classify the reactions.

No, I'm not saying that. That's what I'm wondering---what is the difference?

I read an article from the American Academy of Allergy, Asthma & Immunology called Food Intolerance v. Food Allergy.

It said that a food intolerance "takes place in the digestive system" while "A food allergic reaction involves the immune system" and can lead to dangerous reactions.

Maybe I'm just overly focused on the anaphylaxis. It also says, "Symptoms of allergic reactions to foods are generally seen on the skin (hives, itchiness, swelling of the skin). Gastrointestinal symptoms may include vomiting and diarrhea. Respiratory symptoms may accompany skin and gastrointestinal symptoms, but don’t usually occur alone" which would seem to fit both of our cases.