Geodetic, Rhumb line, or Grid

Geodesic lines measure great-circle distance across the ellipsoid.  This will be the shortest distance between two points on the ellipsoid.  

Rhumb line distance maintains a constant azimuth from the starting point to the ending point.  These are frequently used to plot navigation lines.

Grid distance is straight line distance on the projected surface.  Also called Pythagorean distance.  This type only applies to projected coordinate systems. The source and target coordinate systems must be projected for this option to appear.