Welcome, Chief, to my Village Design and Layouts strategy guide!
A box base consists of one giant box, often with many double and triple layered walls due to the amount of walls left over. These types of bases are very susceptible to archers and wall breakers, due to the fact that the layer(s) of wall surrounding it offers none or relatively no protection.
Improved box bases have one giant layer of wall surrounding the whole base like a regular box base, but in the center (usually) there is normally one "packet," formed by walls, which houses a building or two, often being the town hall or a mortar. This base offers decent protection and is the best type of base for lower level players.
The double box base is not as susceptible to attacks as the Box Base, but it is still vulnerable to archers. It has an outer wall surrounding everything and an inner wall surrounding more important things such as storages and the Town Hall.
A Small Packet Base is a base with numerous "packets," constructed by walls, each packet containing only one building. Although it offers great protection and counters troops really well, the lack of buildings protected by the walls results in an easy 50%. It is often combined with other types of bases and used as an inner layer to enhance the defensive capabilities of a player's base.
Large Packet Bases share similarities to the Small Packet Base, except that each packet contains more than one building inside. This is most commonly used in Hybrid Bases. Large Packet Bases offer a decent level of resistance against Garch and often make it very hard for people using Barch to access the inner layers of your base.