Traditional burial leaves the body intact and placed within a casket. The casket is lowered into an excavated grave, typically supported by a grave liner or burial vault, filled with soil, and a marked by a grave stone / marker. The body can be embalmed to extend the opportunity for a viewing or visitation prior to the funeral and committal services. (language taken from funeralbasics.org)

Flame-based cremation uses flame and heat to reduce human remains to bone fragments, or cremated remains. This is completed with a machine called a cremator. (language from Cremation Association of North America)

Water cremation, also known as alkaline Hydrolysis, uses water-based dissolution process to reduce the human remains to bone fragments, cremated remains --or, more specifically, hydrolized remains-- with alkaline chemicals, heat, agitation, and pressure to accelerate natural decomposition. (language from Cremation Association of North America)

Green burials are designed to cooperate with the natural process of decomposition and to have a minimum impact on the environment. Typically they include no formaldehyde-based toxic embalming chemicals, use of a  biodegradable container in place of a metal or hardwood caskets, no concrete vaults or grave liners, a natural headstone. (language from MN Threshold Network)