The shortest distance between any two points on a nearly spherical surface like the Earth, is along the arc of a great circle connecting the two points.
a straight-line route from one place to another on the surface of the Earth. It is designated great circle because if completed, it circumscribes the entire world. If the world were severed along the line of a great circle it would be cut into two equal parts.
The shortest distance between two places on the Earth's surface. The route follows a line described by the intersection of the surface with an imaginary plane passing through the Earth's center.