The Olympic sport that involves both shooting and running is called modern pentathlon. This multi-discipline event challenges athletes to compete in five different sports: fencing, swimming, equestrian show jumping, and a combined event of pistol shooting and cross-country running. Modern pentathlon tests a wide range of skills and athletic versatility, reflecting the ideals of a well-rounded athlete. Competitors must excel in both mental and physical challenges, making it a unique and rigorous Olympic event.