modern concept states that fermentation has two types which happen under aerobic and anaerobic conditions. final products of aerobic fermentation are CO2 and H2O, whereas, final products of anaerobic fermentation are C2H5OH, CO2 and others organic acid

The definition of fermentation changes with reference to the context i.e.

 In case of metabolism fermentation refers to energy generating processes where organic compound acts as both electron donor and acceptor.

 In context to industrial biotechnology, fermentation is defined as the process by which large quantities of cells are grown under aerobic or anaerobic conditions.

Fermentation is an anaerobic process allowing a microorganism to have the energy necessary for his growth from a sustrate. It's a process where a substrate is uncompletly degraded to acids (succinate, propionate butyrate etc), alcohols (ethanol, butanol) in the abscence of oxygen. Instead of oxygen, the end products of the process are used as electron acceptors. Some organisms can use the same substrate in the presence or absence of oxygen. In the presence of oxygen, the process which is aerobic, convert the substrate to CO2 and H2O. Oxygen is used as final electron acceptor and in this case, the process is aerobic.

Fermentation is used by strict anaerobes and facultative anaerobes (wich use fermentation in the abscence of oxygen and respiration in the presence of oxygen).

There is a kind a anaerobic respiration different of fermentation and where substrate is completly degraded without the use of oxygen (different of aerobic respiration). An other compound (nitrate, sulfate for example) is used as final electron acceptor. Some microorganism can use this process even in the presence of  low concentration of oxygen (aerotolerant microorganisms)

I agree with Arushdeep Sidana. The definition of fermentation changes with reference to the context i.e.

In context to bio-oxidation of metabolism, fermentation refers to one former of energy generating. The organic compound acts as both electron donor and acceptor during the energy generating processes.

In case of industrial bioengineering, fermentation is defined as the process by which large quantities of biological cells (also including plant cell and animal cell) are grown to produce some valuable products under aerobic or anaerobic conditions.