In a strength training sense, high volume is considered low intensity due to the use of less weight whereas low volume is considered high intensity due to the use of heavier weight.
When you look at event duration according to the energy system used:
Phosphagen - very intense
Phosphagen and fast glycolysis - intense
Fast glycolysis - heavy
Fast glycolysis and oxidative system - moderate
Oxidative system - light
High intensity weight training (thus having a high power output), require a rapid rate of energy supplied.
With that said, I believe the "pump" or "burn" should be an occasional part of your workouts in an attempt to increase your lactate threshold (again, allowing us to train at higher intensity).
High intensity (high power output) exercise requires a rapid rate of energy supplied as stated earlier. <--That was an example that you asked for. These exercises rely almost entirely on the energy supplied by the phoshagen system. When that energy system is depleted, fast glycolysis occurs. Now, fast glycolysis occurs....(the original post, 2nd paragraph).