I don't know if there is a specific site to tell you the difference but here is what I know (we have both Celiac disease as well as other food allergies).
Celiac is an autoimmune disease. Gluten causes the body to attack itself causing intentional damage which means problems with nutrition and all the other 300 symptoms of Celiac Disease. There is a Celiac panel that includes 4 tests that the person MUST be consuming gluten to have done. IF the blood work is positive then they usually want to do a follow up biopsy for confirmation of the condition (they look for microscopic villi damage).
Wheat allergy is when the body causes a release of histamine and other substances when the food protein ingested is seen as dangerous and the body attacks it. Symptoms can include vomiting, diarrhea, breathing difficulties, skin issues (hives) and so on. These reactions happen from immediately up to 2 hours after ingestion. Reactions can be fatal, hence the need for epinephrin. Testing for a wheat allergy can be done via a SPT (which you mentioned having) or blood testing. Allergy testing is NOTORIOUSLY inaccurate. There is up to a 50% false POSITIVE rate with these tests which is why it isn't recommended to test unless there has been a reaction (which I very much sounds like you've had!)
Hope that helps a little. Getting ready for bed time here so I'll come back if there is anything more specific I can help with.
This may help: