In the Middle Ages, the bodies of the carts were made by people called cartwrights. The wheels required special skills and were made by people called wheelwrights.
Blacksmith would fix middle age carts and wagons.
Today's weapons are different from those of the Middle Ages for the same reason that we ride in cars instead of carts. Things change.
In the middle ages, as today, a wainwright's job was to build wagons and carts out of wood.
Mainly they walked. Those wealthy enough to afford horses and carts, used those.
In the Middle Ages serfs traveled on foot, by ox drawn carts and boats. If there were lucky they would travel on horses.
In the middle ages
made them
Wood
by hand
People.
sheakspeare
The number one means of travel and transport in the middle ages was walking. Horses were used both as mounts and beast of burden. Horses were quite expensive, especially horses that were fit for military service. Long distance trade used primarily pack horses rather than carts or wagons for transport because of the unreliability of the condition of roads. Carts, both hand carts and horse drawn carts, were used on the local level for transportation of cargo, however. But in many cases porters were hired to simply carry goods.