経路 and 進路: the path through places and the direction of travel
Compare an evacuation route checked on a map with a ship's change of course to the south, separating the path through places from the direction of travel.
An evacuation route checked on a map
経路 (けいろ) identifies the path through places on a journey. 「地図で避難経路を家族と確認した。」 says that the evacuation route was checked on a map with the family.
The object of the check is the path for evacuation. The sentence reports a completed check, without establishing that the family actually evacuated.
The ship's change of course
In a travel context, 進路 (しんろ) focuses on the direction or course of movement. 「船は嵐を避けるため進路を南へ変えた。」 says that the ship changed course to the south to avoid the storm.
南へ identifies the direction of the new course. The change took place, but the purpose of avoiding the storm does not by itself establish that the storm was successfully avoided.
The path through places and the direction ahead
With 経路, read which route the family checked on the map for evacuation. With 進路, read the direction in which the ship changed its course.
Do not restrict 経路 to a route already traveled or 進路 to a future plan. These two travel examples compare the route's path with the direction of movement.
What does 南へ identify in 「船は嵐を避けるため進路を南へ変えた。」?
Show the answer and why
The direction of the changed course. It neither lists every place the ship passed nor establishes that the storm was already avoided.