My son, who is deathly allergic (anaphylactically allergic) to peanut-butter, had a blood test to see if he might have grown out of it (he hasn't; poor kid).
The doctor also order the blood test to screen for specific allergy-causing antibodies to various common allergens, including wheat proteins.
It turns out that his blood had a reaction to albumin (or maybe it was globulin; I can't remember). The Doctor called it a 'wheat allergy' and went on about diarrhea. And Mom and I thought he was just trying to avoid doing the dishes when he'd bolt to the bathroom right after eating: Go figure...
We just look for gluten free because if there is no gluten there is none of the other 4 proteins found in wheat.