They are different things.
Gluten allergy is specifically Coeliac disease, whereas you can have a wheat intolerance and still have to avoid many Gluten free products if they are wheat based.
All this is based on two old friends. One is a Coeliac, which is far more serious, whereas the other is wheat and dairy intolerant. The Coeliac runs the risk of damage to her bowel whereas the wheat intolerant friend just basically gets itchy and develops rashes.
Perhaps some more medically informed person can detail the various proteins concerned where gluten is not the culprit.