Answer
Shear failure occurs when the ring is cleanly cut along the plane of the groove wall; the fracture surface is usually smooth and perpendicular to the ring's face. This happens when the thrust load exceeds the material's ultimate shear strength. Bending failure (or 'Dishing') occurs when the ring deforms elastically and then plastically into a conical shape before ejecting. In bending failure, the ring will be permanently 'cupped' after the event. Shear is a 'strength' failure, while dishing is a 'stiffness' or 'geometry' failure, often solved by increasing the ring's thickness $t$ or using a multi-turn design.