Whats the difference between Celiac Diseas and Allergy to Gluten?

Celiac disease is much more severe than just an allergy to gluten.

Celiac disease is an autoimmune reaction to gluten in which the body attacks the villi of the small intestine in response to the presence of gluten molecules. The result is malnutrition and malabsorption. In the long term, there can be serious consequences ranging from osteoporosis to cancer to death.

An autoimmune response to gluten isn't necessarily limited to the gut. It can also attack the skin (dermatitis herpetiformis) and the brain/spinal cord (gluten ataxia).

Traditional food allergies are IgE mediated. They can be mild in that they cause eczema or hives. They can be life-threatening and cause anaphylactic shock.

Both can kill, though food allergies do so much more quickly.

Celiac Disease is an intolerance to gluten. The villi in the small intestine flatten out and the gluten molecules can leak through the intestinal wall and the body then develops antibodies towards the gluten molecule. The flattening out and lack of villi messes up the digestive system and depending on what part of the intestine it affects the worst can result in any number of problems including some vitamin/mineral deficiencies, diarhea, bloating, gas, etc.
An allergy is a histamine reaction to a substance and results in runny nose, sneezing etc that you associate with taking antihistamines for.
So if you are allergic to gluten then you would develop allergy symptoms and end up taking allergy medicine with antihistamines for it.
The only treatment for celiac disease is to go on a strict gluten free diet and allow the small intestine to repair itself and then continue to stay on the diet to keep from reinjuring it.
Gluten sensitivity is like being preceliac where consuming gluten causes the symptoms of celiac disease but only if you consume too much. Also, the blood work and endoscope won't show celiac disease but if you are gluten sensitive you will just feel much better not consuming it.
You might hear a person with celiac disease say they are allergic to gluten when talking to a restaurant waiter or an acquaintance because sometimes it is easier to get the point across that you can't have gluten because people understand the word allergy and avoiding allergens better than the word intolerance.