Cities and villages are a type of area in the world. They both serve and share the same functions and services except a few differences. They are inhabited by non-hostiles NPCs.
Inns are in both cities and villages. There, you can recruit NPCs, get new quests, rest, buy some booze and participate to drinking contests. The innkeepers can also inform you about rumors of quests, locations and artifacts in the world.
Only in the cities, arenas can be a fast way to earn money. You can fight with your companions against various types of enemies, participate in the tournament and challenge your companions on a duel. All of this can be asked to the arena master, next to the entrance.
Village house are in both cities and villages. They serve as town halls where you can get a quest from the mayor. In cities, they are bigger and there is an other office where a clerk works.
Barracks are in both cities and villages. Although you can't enter them, it is assumed that they host the local guard. Near the entrance, the captain of the guard can guve you quests.
Blacksmith are in both cities and villages (may not always be in a village). There, you can purchase and sell equipment.
Alchemists are in both cities and villages (may not always be in a village). There, you can purchase and sell potions.
Merchants are present in both cities and villages. There, you can purchase and sell all kind of items.
Food sellers are present in both cities and villages. There, you can purchase and buy food.
Note: the only differences between cities and villages are their services and their icons on the map.