Here are some other names, depending on the specific type:
* Sulky: A lightweight, two-wheeled carriage used for racing.
* Cart: A simple, open carriage with two wheels.
* Gig: A small, two-wheeled carriage for one or two people.
* Phaeton: A four-wheeled carriage with a folding top.
* Surrey: A four-wheeled carriage with a fixed top.
The term "buggy" is the most common and general term for a one-horse carriage.