When were cars invented?
Nicolas Joseph Cugnot built a steam-powered road machine in Paris, France in 1769. His second version, built in 1771, still exists. Others followed but these too, were considered "road locomotives" or "steam tractors". In short they were designed to pull trolleys or freight wagons.
The technical problem with these early machines (beside the lack of roads) was that engines of the era were not powerful enough to move the amount of fuel it took to keep them running. In time, smaller stationary engines were used in manufacturing and farming however.
The first vehicle designed for "personal" use was the three-wheeled 1891 Benz in Germany. Other manufacturers followed quickly in Europe. Interestingly, at that time "car" was assumed to be a railroad car. The term "car" was used as an adjective to the body style through (about) 1910, ie: touring car.
"Automobile" was a French term generally accepted in the United States from 1898 when there really weren't many on the road. Shortly thereafter "automobile" gained acceptance overseas too.
The term "horseless carriage" was used at least as early as 1896 in the United States. Thereafter it meant a vehicle built by a small company or individual because, it was usually nothing more than a carriage the "inventor" added an engine to. Large companies building expensive "automobiles" never used the "horseless carriage" label.
Sometime around 1915 when automobiles were perfected (according to the advertising of the day) the public started using "horseless carriage" to mean any obsolete vehicle.