For the benefit of readers, a "stage" originally referred to the distance between stops on a route. Through constant misuse of the word, the term "stagecoach" evolved.
"Stagecoach" has always been loosely applied to any four wheeled vehicle pulled by horses or mules, the primary requirement being that it was used as a public conveyance, running on an established route and on a schedule.
The immediate ancestor of the stagecoach was the stage-chaise which was a fast carriage for transporting passengers in the 18th and early 19th centuries. It usually had a closed body on four wheels, sat two to four people, and was drawn by two or four horses.