Difference between scale and height in a gameobject with charactercontroller

The gameObject scale will affect all it's components, such as the renderer (the character will appear bigger) or the capsule collider, and even it's children components.

In the other hand, the character controller height will just affect the way this component behave, meaning if your character controller height is higher than your gameObject, it won't touch the ground ! It has nothing to do with other components or children.