The difference between Local and Global Texture Coordinates, is in this case, that when you move the Cube in Object Mode, the Displacement doesn’t change when using Local, but it does change when using Global. This is, because the Cube changes its position compared to the World Origin, but not compared to its own Origin.
The fact that you see nothing happening in your first picture, is due to the fact that the Displacement happens to be zero at the Origin. And any number times zero is zero, so changing the strength makes no difference;)
Try reducing the Size of your Clouds Texture (that you are using for your Displacement Modifier) and you will see the effect of the Displacement.
