A coach. Rattle and prad; a coach and horses.

–From the 1811 Dictionary of the Vulgar Tongue.

A coach, cart, or other wheeled carriage.

–From the 1811 Dictionary of the Vulgar Tongue.

A hackney coachman.

–From the 1811 Dictionary of the Vulgar Tongue.

Listed in the Vulgar Tongue as jarvis, but also seen in books as jarvey.

(An abbreviation of the word DILIGENCE.) A public voiture or stage, commonly a post chaise, carrying three persons; the name is taken from the public stage vehicles in France and Flanders. The dillies first began to run in England about the year 1779.

–From the 1811 Dictionary of the Vulgar Tongue.

Early bicycle without pedals, you sat on it and pushed along the ground in strides with your legs.

Merriam-Webster

A lightweight wheeled vehicle propelled by the rider.

Wikipedia

A Hansom cab is a kind of horse-drawn carriage first designed and patented in 1834 by Joseph Hansom, an architect from Hinckley, Leicestershire, England. Originally known as the Hansom Safety Cab, its purpose was to combine speed with safety, with a low center of gravity that was essential for safe cornering.

Merriam-Webster

A light 2-wheeled covered carriage with the driver’s seat elevated behind — called also hansom cab.

Wikipedia

Beginning in the 17th century, they were originally horse-drawn carriages, later modernized as hansom cabs (1834), that operated as vehicles for hire.

Merriam-Webster

A coach kept for hire; especially : a four-wheeled carriage drawn by two horses and having seats for six persons.

A hack can also be used to describe a horse:

Merriam-Webster

A horse let out for common hire (2) : a horse used in all kinds of work b : a horse worn out in service : JADE c : a light easy saddle horse; especially : a three-gaited saddle horse d : a ride on a horse

Wikipedia

A cabriolet was a light, two-wheeled horse-drawn carriage with a folding ‘calash’ top, seating two persons behind the driver’s box. Developed in France in the early 19th century, the vehicle quickly replaced the heavier hackney carriage as the vehicle for hire of choice in Paris and London. The modern term (taxi)cab comes from “cabriolet” via “Hansom cab”.

Merriam-Webster

A light 2-wheeled one-horse carriage with a folding leather hood, a large apron, and upward-curving shafts.

Merriam-Webster

A light closed horse-drawn carriage with the driver outside in front.

Wikipedia

Invented by Henry Brougham, 1st Baron Brougham and Vaux, Lord Chancellor of Great Britain, a brougham was a four-wheeled horse-drawn carriage of the 1800s. It had a low body with a box seat in front for the driver. In the rear was seating for two or four with two doors.

Merriam-Webster

A four-wheeled carriage with a driver’s seat high in front, two double seats inside facing each other, and a folding top over the back seat.

Wikipedia

A barouche, also known as a calash or calèshe, was a fashionable type of horse-drawn carriage in the 19th century. It was a four-wheeled vehicle with two double seats, a collapsible hood over the back seat and an outside box seat at the front for the driver. It was drawn by pairs of high-quality horses and was used principally for leisure driving in the summer.

The word barouche is an anglicisation of the German word barutsche, via the Italian biroccio and ultimately from the Latin birotus, “two-wheeled”. (The name was thus something of a misnomer, as the carriage had four wheels; but it had evolved considerably since the name was first coined.)