Geodesic lines measure great-circle distance across the ellipsoid. This will be the shortest distance between two points on the ellipsoid. Geodesic lines only apply to Geodetic coordinate systems (Latitude/Longitude).
Rhumb line distance maintains a constant azimuth from the starting point to the ending point. These are frequently used to plot navigation lines. Rhumb lines only apply to Geodetic coordinate systems (Latitude/Longitude).
Grid distance is straight line distance on the projected surface. Also called Pythagorean distance. This type only applies to projected coordinate systems.
CCG (Cartesian Color Grid) is a type of coordinate system specific to air traffic control. For more information, see the page on CCG.