What is the difference between IgE and IgG mediated allergies and is it significant?

IgE
IgG

The difference is significant because in some studies Crohn's patients have not demonstrated IgE allergies while showing significant IgG mediated allergies.  Testing with IgE (skin), therefore, does not eliminate the possibility of food-based allergies.
See "Gut mucosal response to food antigens in Crohn's disease" in Alimentary Pharmacology and Therapeutics (2002)
"The role of food-specific IgE has also been examined in a study of sera from Crohn's disease patients, healthy controls and allergic subjects. IgE binding to food antigens (yeast, corn, celeriac, wheat) was assessed by an immunodot assay.²⁷ Levels of IgE/IgG anti-IgE immune complexes were determined. In Crohn's disease sera, no food-specific IgE could be detected, but levels of immune complexes of IgE and IgG anti-IgE autoantibodies were significantly increased compared to healthy controls. pH treatment of purified IgE/IgG anti-IgE immune complexes resulted in a significant increase in specific IgE to yeast, corn, wheat and celeriac, detected by radioallergosorbent test, only in the serum sample purified from allergic subjects. After pH treatment of Crohn's disease immune complexes, specific IgE levels still remained very low. Thus, even if IgE seems to represent an autoantigen in Crohn's disease, it is unlikely to specifically participate in the pathophysiology of the putative food adverse reactions." [emphasis mine]

How do food allergies affect the gastro-intestinal system?

"Gastrointestinal Manifestations of Food Allergies in Pediatric Patients" in Nutr Clin Pract (2005) 
"Foods that account for 90% of allergic reactions in children are cow's milk protein, eggs, peanut, soy, tree nuts, fish, and wheat. Food allergy can manifest as urticaria/angioedema, anaphylaxis, atopic dermatitis, respiratory symptoms, or a gastrointestinal (GI) disorder. GI allergic manifestations can be classified as immunoglobulin E (IgE) mediated (immediate GI hypersensitivity and oral allergy syndrome); “mixed” GI allergy syndromes (involving some IgE components and some non-IgE or T-cell-mediated components) include eosinophilic esophagitis and eosinophilic gastroenteritis. Non-IgE-mediated or T-cell-mediated allergic GI disorders include dietary protein enteropathy, protein-induced enterocolitis, and proctitis. All these conditions share a common denominator: the response of the immune system to a specific protein leading to pathologic inflammatory changes in the GI tract. This immunological response can elicit symptoms such as diarrhea, vomiting, dysphagia, constipation, or GI blood loss, symptoms consistent with a GI disorder."