Both system dynamics (SD) and discrete-event simulation (DES) are used to help understand and explain puzzling real world dynamics.  But what are the similarities and differences between these two approaches and which should be used in a specific circumstance?  These are questions few have ventured to answer.  In this research the two approaches are compared by developing an SD and DES model of the same problem situation, a fishery.  An SD expert and a DES expert separately develop a model of the fishery through a number of evolutionary steps.  At each step differences in the representation and interpretation of the models are identified.  Overall it is apparent that while SD illuminates 'deterministic complexity', DES illuminates 'constrained randomness'.  Either or both may be important in understanding and explaining puzzling dynamics.  SD and DES should therefore be seen not as opposing modelling approaches, but as complementary.