What's the Difference Between a Wagon and a Carriage?

What's the correct word for this onetime local vehicle and why would you choose that word? The answer is just barely visible in this photo.

Was the canopy an add-on? It seems a bit tacked-on to the outside of this craft, does it not? If this vehicle was owned and not rented, DD imagines that it belonged to a wealthy family who could afford to maintain a vehicle not of immediate practical use, but only for leisure.

Hmm, carriage or wagon?