Cart

The most inexpensive and widely used vehicle, a cart is made out of wood and used to transport people or cargo. It's got two wheels and it is open to the elements but usually has two or three raised sides to stop things from falling out. There are various sizes of carts, the smallest of practical use being the handcart which is pulled by one or two people. This one is most commonly used by people who can't afford some kind of beast to pull the cart for them, like produce farmers or less well to do merchants. However, in some settlements a lot of the streets are too narrow for beasts of burden and larger carts and then handcarts are used by people no matter their wealth status. Though if someone is rich enough they'll have servants pulling the carts for them.
Larger carts pulled by beasts of burden such as horses or oxen for example are typically used by farmers or merchants with enough coin to keep draught animals. They are also popular as a fairly cheap method of travel as some settlements have special stables where you can rent carts and horses. Or it is sometimes possible to pay a bit of money to a passing farmer or merchant to be allowed to hitch a ride.
Then there are types of carts that are typically not used for any practical purposes, like the very small carts pulled by dogs or goats. These are most often used to entertain small children. Though in some cases when someone can't afford a larger animal and don't want to carry smaller things they use this type of cart. A not all too rare sight is an old woman walking by, leading a goat or a dog pulling a small cart with her wares for the market or shopping purchases.

Rarity

Common