All objects ‘live’ in their own space (their own coordinate system where the origin is the object’s origin).
This means, all vertices from an object are placed in relation to the object’s origin.
If you have an edge, that looks to have a length of 1 meter in world coordinates but it’s object scale is 2.0, it means that in the object’s space that edge is in fact 0.5 meters … Everything that is using the object’s space will say that 1 meter is in fact 0.5 meters, and all other objects with a 1.0 scale will disagree.
In case of textures using the object’s coordinate space, the same will happen. You might want to draw a circle in a space scaled to [2.0, 0.5, 1.0], but the result will be an ellipse even if for the object, the circle is perfect (because as the viewer, you’re in the world space, and your dimensions are different from the object’s dimensions);
more on this…