Are PCB spreading inductance and loop inductance the same thing?
It's just the inductance due to the plane over the distance (2).  So it is part of the loop inductance.

From Intel AN 574 (they have nearly the same picture):


  The spreading inductance is design dependent and scales as a function
  of the dielectric thickness (h) between the power/ground plane. It is
  determined by the spatial location (d) of the capacitor with respect
  to the load. Minimizing the dielectric thickness (h) reduces the
  capacitor location sensitivity and allows you to place the capacitors
  farther away from the load.