Both the sphincters are associated with gastrointestinal tract. Sphincter is a strong band of circular muscles to close an opening or a passage.
Sphincter of Oddi is located at the exit of ampulla of Vater in duodenum.
We know that duodenum receives bile from liver and pancreatic juice. These are respectively reaching Ampulla of Vater by common bile duct and duct of Wirsung (=major pancreatic duct).
Ampulla of Vater opens in duodenum to pour digestive juices, and the opening is guarded by Sphincter of Oddi. It also prevents entry of intestinal content in ampulla of Vater.
Ileocaecal sphincter (often called a valve) is the last portion of ileum which thickens due to presence of circular muscle band and the sphincter prevents colonic bacteria, etc to enter in ileum.