Hearse, often referred to as a funeral coach, originally referred to the horse-drawn carriages that conveyed the casket to the place of burial. The use of the word began in the 17th century. The word "hearse" comes from the Middle English "herse," which referred to a type of candelabra often placed on top of a coffin.
Hearses remained horse-drawn until the first decade of the 20th century, when motorized hearses began to appear. Nobody's quite sure what year these motorized hearses were first put into use, but it was most likely between 1901 and 1907. Gas-powered hearses became the norm by the 1920s.
It was not uncommon in the early and middle parts of the 20th century for hearses to serve as both funeral coach and ambulance, depending on the immediate need of the community. Such vehicles, once common in small towns, were known as combination coaches. Regulations for ambulances became stricter after the 1970s, however, and now it's rare for one vehicle to serve in both roles.
This beautiful 1860 horse drawn hearse was on display at the Rogers, AR Historical Museum during the "Victorian Era Mourning" exhibit in 2009.
If interested in seeing how a modern day hearse is made this is a good video.