Gluten actually describes a set of related proteins that are found in the seeds of many grains.
Gluten allergy sufferers and those with celiac disease know to avoid wheat, barely, rye and oats because of the gluten. More specifically, these four grains have very similar types of gluten that trigger celiac disease. For those with a gluten allergy rather than celiac disease, it is possible that one or two of these grains is worse than the others. Equally, it could be that other grains, such as corn or sorghum, have a type of gluten that is worse for your specific gluten allergy.
Some celiacs find that other grains besides the big four make them feel a little off.
Prolamin is considered to be the trigger for celiac disease. Prolamin, glutenin or both might be the problem for a gluten allergy, again, depending on your allergy.
Corn also contains prolamin, but it is called zein and is not considered to be a trigger for celiac disease.
Another way of looking at gluten is what it does to baking. Gliadin is responsible for the wonderful baking properties of wheat, providing wheat-based baking with strength and elasticity of the batter which allow a huge variety of products to be formed. Since gliadin is not considered a celiac trigger, a type of wheat may one day be bread (no pun intended) that with all gliadin and no prolamin.
This would be of great benefit to celiacs, assuming it works, but may or may not help avoid triggering gluten allergy symptoms.