Are there different types of loop ileostomy?

Not really. A loop ileostomy is an ostomy where both upstream and downstream ends of the bowel come through the same opening in the abdominal wall. It can be different in terms of what segment of bowel is used. It usually allows for a simpler closure of the ileostomy and a shorter recovery time following pouch surgery.
No. An ileostomy is either a loop or a single end but no different types of loop ileostomy.