height: 100% will match the height of the element’s parent, regardless of the parent’s height value.
height: inherit will, as the name implies, inherit the value from it’s parent. If the parent’s value is height: 50%, then the child will also be 50% of the height of it’s parent. If the parent’s size is defined in absolute values (e.g. height: 50px), then height: inherit and height: 100% will have the same behaviour for the child.