I don't have time to type up a good answer, but I wanted to throw in that the difference between orthogonal and isometric maps goes beyond visual perspective in games. Maps are not just images or views in games, but have many things which happen within them and these things work differently between the two map types. Many of these differences are not seen by the user. For example, an algorithm used to determine trajectory of an arrow being shot by a player can be different between the two map types. The differences in the sprite of the arrow/shot can be considered a matter of visual prospective, but the math differs as well and is outside of the players view/perspective. While this may not answer "the" difference between the two, it describes one of many ways that the two are different outside of visual perspective.
It's also worth noting that maps in games often use many levels and groups of objects to create a specific view. How objects interact between these different layers and groups is different in the two maps as well (such as collision detection) and is typically easier when orthogonal.