[RPG] the cargo capacity of a Cart versus a Wagon

Carts have a single axle (two wheels), wagons have a double axle (four wheels).

The rules provide no detail about the differences between a cart and a wagon beyond what you have likely already found:

\$\begin{array}{|l|c|l|} \hline \textbf{Item} & \textbf{Cost} & \textbf{Weight}\\ \hline \text{Cart} & \text{15 gp} & \text{200 lb.}\\ \text{Wagon} & \text{35 gp} & \text{400 lb.}\\ \hline \end{array} \$

From this information we can sensibly deduce that a wagon, being heavier, is likely larger than a cart and thus capable of carrying more - but exactly how much more we don't know.

With neither 'wagon' or 'cart' defined more explicitly in game terms we can instead draw from the plain english meanings of these words for further insight. While in common usage these words are often used interchangably, Wikipedia states:

A cart is a vehicle designed for transport, using two wheels and normally pulled by one or a pair of draught animals. It is different from a dray or wagon, which is a heavy transport vehicle with four wheels and typically two or more horses, or a carriage, which is used exclusively for transporting humans.

This information loosely tallies with the stats we've got for carts and wagons in 5e and so it seems reasonable to conclude that wagons and carts in 5e are similar to wagons and carts in the real world.

There is nothing to prohibit either size vehicle from having a rounded tarp roof.

It can pull a vehicle weighing up to 2100 lbs.

The weight limits for pulling a vehicle and dragging an object are both multiples of carrying capacity. Due to the mule's Beast of Burden trait, its carrying capacity is 2 × 15 lbs × Strength = 420 lbs.

In this case the animal is pulling a vehicle, so the limit is 5 × carrying capacity = 2100 lbs for the vehicle and its contents combined.

Speed reduction for pushing/dragging a heavy object only applies for the more general pushing/dragging rule, so the mule gets its full speed when pulling a wagon. Wheels, man. They're actual magic.

(Note that the speed reduction for a heavy object is not a "5-foot speed decrease"; your speed becomes 5 feet, unless it was already less than that.)