Putrefaction is the decomposition of animal proteins, especially by anaerobic microorganisms, described as putrefying bacteria. Decomposition is a more general process. Putrefaction usually results in amines such as putrescine and cadaverine, which have a putrid odor. Material that is subject to putrefaction is called putrescible.
In alchemy, putrefaction is the same as fermentation, basically meaning to allow the substance to rot or decompose, sometimes with a small sample of the desired original pure material to act as a "seed".
The exact rate of putrefaction is dependent upon many factors, such as weather, exposure, and location. Thus things like refrigeration at a morgue or funeral home can retard the process allowing for burial in three days or so following death without embalming.