Chief and captain are both high-ranking officials/leaders. A chief is usually a leader of a group or a clan, such as chief of police or chief of a tribe. A captain is usually a leader in the military or commander of a ship.
Ex: Sitting Bull was a famous Native American chief of the Teton Sioux tribe.
Ex: Captain Phillips is a movie based on a true story of a ship hijacking by Somali Pirates and how Captain Phillips survived it.