Any open-air four-wheeled sporting vehicle with seating for two is classified as a phaeton. Phaetons could accommodate one, two, or four horses. There were many variations of the phaeton. A popular version was the high-perch or highflyer phaeton, made fashionable by the Prince Regent. Its exaggerated elevation often made it dangerously unstable, which, naturally, made it popular among sportsmen.
The print, showing a high-perch phaeton, is from the magazine Gallery of Fashion, August 1794. (It's so high off the ground, one has to wonder how the ladies got up into it!)