Hey I think you have this backwards and just want to clarify so make sure other people don't get confused and cause harm. Gluten is a protein found in wheat, yes. But that does not mean wheat is gluten - there is no logic in that. People who are allergic to wheat have an allergic reaction to the entire wheat itself. Typically food allergies are a response to a protein found in that food, so if you test positive for a wheat allergy but not celiac disease you are probably reacting to a different protein found in wheat (this is the case for me). People who are allergic to the gluten protein are allergic to the gluten protein.
I'm not sure what you mean by the traditional sense of an allergy, but I know that alcohols can be distilled to the point where gluten is present in such a small amount that it is considered gluten free. This does not say much to any other proteins in wheat that others may be allergic to, so I would make sure to double check. The gluten protein may be gone, distilled, removed, or what have you, but that does not necssarily mean it is safe to consume if you have a wheat allergy.
Bottom line, wheat does not equal gluten.