Pathfinding on isometric grids

People sometimes ask about pathfinding on isometric grids. This is the wrong way to look at it.

You're finding paths in the game world. Isometric is not part of the game world. Isometric is how you look at the game world. Consider the shortest path from New York to San Francisco. Does the shortest path depend on how you hold the map? No! The person looking at the map does not matter. The shortest path is the same no matter how you are looking at the map.

Here's an animation showing the way to think about isometric grids. Note that the map coordinates and the path don't change; it's only the way we look at it that changes.

0,0
0,14
14,14
14,0

Pathfinding runs on the game map. The game map coordinates shouldn't depend on "top down" or "isometric".