What is the difference between hilum of the lung and root of the lung?
Short answer: Hilum is an area(has only 2 dimensions) where as root is a body( has 3 dimensions).


  The root of lung is a short broad pedicle connecting the medial surface of the lung with the mediastinum. It consists of structures entering and leaving the lung at hilum. The root of lung is surrounded by a tubular sheath derived from the mediastinal pleura.


and


  The hilum is the area on the mediastinal surface of the lung through which structures enter or leave the lung.


Source: pg no 239

Consider the following image( edited by myself):

If the cylinder is root of lung then lateral opening(blue) is hilum.



The region bounded( within the limits of pleural membrane) by those two planes is root of lung and the area bounded by the lateral plane is hilum.