Is there any difference between a wheat allergy and celiac disease?

Yes: In wheat allergy, there is an immune response that involves making an allergic antibody (called ige) against wheat proteins. This causes allergic inflammation, which leads to immediate, rapid reactions to wheat. In celiac, there is also an immune reaction, but it is slower and lasts longer. So wheat allergy tends to be rapid reactions that resolve quickly, while celiac is a long, slow process.

Allergy vs celiac: A wheat allergy is the symptoms that occur when you make ige antibodies to wheat. Celiac disease is the symptoms that occur when your body makes IgA antibodies to the gluten in wheat, rye and barley. The symptoms can be similar in that both can cause bloating, abdominal pain, loose stools, etc. Allergies can cause anaphylaxis and celiac raises cancer risk, so it helps to find out which you have.

Differs considerably: Wheat as a composite of many proteins all of could trigger a simple allergic response like hives or worse. (quick issue) The reaction clears when the protein trigger is gone. In celiac disease the body produces antibodies to various gluten proteins that mistakenly attack intestinal tissue & cause tissue damage. That tissue injury can continue as long as there are circulating antibodies(months)