We have three metabolic energy systems that we use, phosphagen, glycolysis and aerobic respiration. The two former systems produce energy, ATP, in the absence of oxygen, anaerobic, and the latter uses oxygen, aerobic. The difference in these systems is the speed at which they can produce energy, the intensity at which you can perform and the sheer amount of energy that is produced from one simple sugar molecule, glucose.
The phosphagen system, also known as phosphocreatine system, is the immediate source of energy and can produce about 12-15 seconds worth of energy for HIGH intensity exercise. It is predominantly used in explosive burst like sprints of 100 meters, heavy resistance training and fast twitch movements like squat jumps.
Glycolysis is the intermediate system and can produce energy for about 2 minutes of moderate to high intensity exercise. It yields 2 net ATP per molecule of glucose. Picture 400m and 800m runs and exercises done via circuit training.
Aerobic respiration can steadily produce energy for prolonged periods of time if given enough sugar or fat and most importantly, oxygen. It allows for moderate to low intensity steady state exercise. This system yields a net 38 ATP per molecule of glucose and wil keep you going for miles and miles. This means that aerobic respiration is the most efficient system for producing energy by up to 19 times, given the same amount of sugar.
Moral of the story, if your aim is to burn the most calories, stick to short explosive bouts of energy and concentrate your efforts in the anaerobic side of your metabolism for a less efficient use of your stored energy.
For more information check out this video on the subject!