How are gluten intolerance and celiac disease different?

Celiac is an allergy: Celiac disease is gluten allergy, a strong allergic reaction to gluten (a protein in grains such as wheat, barley, malted barley, rye, spelt, etc...). Gluten intolerance is not an allergic reaction, but an intolerance of gluten that leads to tummy symptoms such as gassiness, bloating, loose stools, etc... Gluten intolerance does not cause damage to the intestinal lining like celiac disease does.

No difference: You can split hairs and say that if you have chronic diarrhea, weight loss, malnutrition when eating foods with gluten, that you have celiac disease and any milder symptoms of bloating, recurrent abdominal pain etc that you have gluten intolerance but the solution to both is a gluten free diet.