A loxodrome or rhumb line is a track of constant bearing, that is, it crosses all meridians with a constant angle.
An orthodrome is a track corresponding to a great circle segment.
The smallest distance between two locations on a spheroid is obtained by flying a great circle segment (or orthodrome). For example, the distance between Paris and New York is about 3.9% longer along a rhumb line than along a great circle path. However, flying along a great circle implies, in general, changing the bearing constantly in order to comply with the corresponding great circle track. Thus, rhumb lines are easier to fly (hand flying, anyway!). It is relevant to observe that a great circle track can be approximated by several rhumb line tracks. This allows to take advantage of both navigation techniques; shorter distances and constant bearing navigation (well, with a few turns).
The mobile application allows you to determine the (true) bearing and the distance between two positions given their geographic coordinates (Lat/Long). Have fun!