I sometimes use the two terms interchangeably when explaining it: “My roommate has a gluten allergy — he’s allergic to wheat.” But the two really aren’t the same thing.
If you have a gluten allergy (also known as celiac disease), the cause of the problem is a mixture of protein fragments in wheat and other common cereal grains like rye, oats, and barley. Different kinds of wheat, like semolina and spelt, are all unsafe. If gluten is your problem, you’ll have to eat other grains, like corn, rice, millet, sorghum, and quinoa.
If you have a wheat allergy, the cause of the problem is the protein in the wheat itself. Rye, oats, and barley may all be safe to eat.
As with many allergies, your sensitivity may range from mild to strong. One of my roommates has celiac disease and is highly sensitive. He can’t eat any foods that are processed in plants that also process wheat products. If a utensil touches something with wheat and then his food, he’ll have a reaction.
In order to try to prevent cross-contamination, we have two butter dishes, two toasters, two pizza cutters, and even two George Foreman grills! Everything is clearly marked GLUTEN FREE, so we know to keep the wheat (and other dangerous products) out of the way. Just the other morning I accidentally used the wrong butter when I made breakfast, so I had to start over with a fresh pan and clean spatulas. We try to be really careful if we go out to eat — some restaurants like P.F. Chang’s and Red Robin do offer a gluten-free menu, but with others, he’s taking his chances.
I also have a friend who is allergic to wheat, but her allergy is relatively mild. She can eat products that contain wheat if they’re pretty low on the ingredient label, but for the most part she sticks to other grains just to be safe.
Some resources for folks with gluten allergy or wheat allergy: