In this paper, the special place of Zipf's law and Pareto's law amongst other classical informetric laws (such as Bradford's graphical and verbal law, Weber-Fechner's or Brookes', Leimkuhler's and Mandelbrot's) is revealed and explained. Equivalencies amongst some of these laws are proved. We also determine the conditions under which Bradford's graphical law is a special case of Bradford's verbal law.