The difference is just between the energy systems used.
Short bursts of action (sprinting, heavy lifting) use the ATP-PC system or anaerobic glycolysis, which aren't dependant on oxygen.
Longer exercises (jogging, high rep lifting) use aerobic glycolysis and oxidative phosphorylation to produce ATP for energy.
The ATP-PC system just uses ATP and Creatine to produce energy. Aerobic and Anaerobic glycolysis uses muscle glycogen. And oxidative phosphorylation uses fats predominantly.