What is the difference between aerobic and anaerobic respiration?

Both aerobic and anaerobic respiration involve chemical reactions which take place in the cell to produce energy, which is needed for active processes.
Aerobic respiration takes place in the mitochondria and requires oxygen and glucose, and produces carbon dioxide, water, and energy. 
The chemical equation for is:
C6H12O6 + 6O2 → 6CO2 + 6H2O 
(glucose + oxygen -> carbon dioxide + water)
Anaerobic respiration also produces energy and uses glucose, but it produces less energy and does not require oxygen. This is useful in tissues which have a high energy demand such as in working muscles, in which there is not enough oxygen to produce all the energy needed by using aerobic respiration alone. Anaerobic respiration takes place in the cell cytoplasm and produces lactic acid. The chemical equation is: 
C6H12O6 -> 2C3H6O3 (Glucose -> Lactic acid)
The lactic acid then needs to be oxidised later to carbon dioxide and water afterwards to prevent it building up. This process requires oxygen and therefore following anaerobic respiration there is oxygen debt in the cell, as oxygen is needed to break down the lactic acid produced.