Fermentation extends glycolysis, the first stage of metabolism, to produce usable energy, while anaerobic respiration uses molecules other than oxygen to complete the metabolic cycle. Both are methods used to produce ATP, the energy currency of the cell, in the absence of oxygen. Anaerobic respiration produces more energy than fermentation, but is used by fewer organisms in very specific situations.
Fermentation is an extremely common way of gaining energy from food in the absence of sufficient oxygen. Many microorganisms use fermentation, like yeast producing ethanol, or animal, fungal or bacterial cells producing lactic acid. Lactic acid fermentation is what occurs when an animal, such as a human, must exert their muscles or other functions beyond the oxygen it can supply. Their cells then use glycolysis to transform the NADH molecule into the NAD ion, permitting the production of small amounts of ATP. This process is very inefficient relative to normal cellular respiration.
Anaerobic metabolism exists mostly in bacteria, including the bacteria in many animal intestinal tracts. These organisms use electron acceptors other than oxygen to complete their metabolic cycles. Intestinal organisms commonly use carbon dioxide as one electron acceptor. Using carbon dioxide in this way produces methane or acetic acid, depending on the organism.