How can one blockchain with the same block heigth as another, have more Proof-of-Work I am reading Andreas M. Antonopoulos's book and In chapter 10 - Assembling and Selecting Chains of Block he writes:


  Under most circumstances this is also the chain [main chain] with the most block
  in it, unless there are two equal-length chains and one has more
  Proof-of-Work.


Can somebody explain how this is possible? How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets? Not sure how this could happen, but this is my only hypothesis.
How can 2 chains with the same length have different cummulative Proof-of-Work? Is it because they might include block that were mined with different difficulty targets?


That is correct. The bitcoin protocol actually follows the chain with the highest accumulated proof-of-work, not the largest block height. 

I believe the original implementation followed the largest block height, but that left the network open to certain attacks, so it was soon changed to largest accumulated proof of work.