Celiac disease is also known as non-tropical sprue or celiac sprue. It is a hereditary auto-immune disease.
(Tropical sprue is a disease with basically the same symptoms as Celiac disease but the cause is unknown)
Collagenous sprue has been defined as a (small) intestinal mucosal disorder that causes multiple nutrient deficiancies, weight loss, chronic diarrhea and severe malabsorption. It is believed that Collagenous sprue is the result non-responsive Celiac disease.
In other words, if a Celiac on a gluten free diet does not have improvement in the condition of the villi in the small intestine, they can develop collagenous sprue.
Collagenous sprue is rare.