Celiac disease:
A disorder in which gluten causes your immune system to attack your small intestine; over time, the attacks can damage the lining of your intestine.
Non-celiac gluten sensitivity:
Also called gluten intolerance, the condition causes celiac symptoms -- like stomach pain, bloating, and diarrhoea -- but doesn’t damage your small intestine.
Wheat allergy:
Your immune system fights gluten like a virus or bacteria; if you eat it, you may have trouble breathing, a skin reaction, or problems digesting.
https://www.medicinenet.com/gluten_foods/article.htm