Types of Nappies

All reusable nappies consist of some absorbent fabric inside a waterproof outer. They are just variations on this theme.
The choice is yours.
Even a practiced eye is unlikely to be able to tell which type your baby is wearing, unless it has a label or recognisable print/design. 

All in One Nappies (AIO)

An All-In-One (AIO) Nappy has the absorbent material sewn in to the waterproof outer. They might also include a stay-dry layer and/or a booster which folds out for quicker drying. 
Boosters can be added to increase absorbency.
This is arguably the simplest type of nappy to put on, but are often slow to dry and are the most expensive type.
The whole thing needs to washed and line dried at every change.

Pocket Nappies

A pocket nappy has a pocket opening at the back or front of the nappy in which you stuff an absorbent insert or two. These are fleece lined on the inside, to create the pocket between the lining and the waterproof outer. Inserts can be swapped and changed depending on your needs. 
These are cheaper than AIO's, quicker to dry as the inserts remove completely, and more customisable.
All the parts need to washed and dried at every change. Some inserts can be tumble dried, but the outer must be line dried.

Shaped Nappies

A shaped nappy is absorbent fabric shaped to fit, and fastens with aplix or snaps underneath a waterproof wrap, which is purchased separately. 
Shaped nappies are the most absorbent option, and the best choice for night time. They can often be tumble dried (on cool).
Extra absorbency can be added either inside the nappy or between the nappy and the wrap.
Wraps are necessary for both flat and shaped nappies, and can be used roughly 4 times between washes.

Flat Nappies

A flat nappy is the most basic type of nappy - a terry square or a prefold, which can be folded around a baby's bottom and secured with a fastener, or simply folded in a 'pad fold' and laid in a waterproof wrap. 
Flat nappies are the most economical option, and  can often be tumble dried.
Wraps are necessary as a waterproof outer layer, and can be used roughly 4 times between washes.

All in 2 Nappies (AI2)

A cross between a flat nappy and an all in one. The specially designed inserts of an all in two nappy attach to the waterproof outer usually with carefully placed snaps. Extra inserts can be purchased to swap each change, reusing the outer several times before washing. These can pack smaller compared to other types, making them good for travelling light when out and about. 

Wool Covers

100% hand wash only wool is knitted into a cover to be worn over a shaped nappy or a fastened flat nappy.
A wool cover is a plastic free alternative to a nappy wrap, and is lanolised to make it water resistant. Lanolin is the natural waxy substance which is washed out of a sheep's wool when it is sheared.
We wash lanolin back into the wool cover to make it water resistant. Lanolin is naturally moisturising to the skin, and is safe next to baby's skin. 
The natural properties of the wool make it antibacterial, and wool covers only need to be washed every few weeks (by hand), hanging them up inbetween uses to air out.
Whilst they take a bit of work to get ready, and make for a bulky shape, they are fantastic options for wearing over a night nappy, as they are breathable, allowing moisture to evaporate, and leave no sock marks on baby's skin.

Hybrid Nappies

A disposable insert which is placed in a reusable wrap. Some stick on with a mild adhesive. Some are biodegradable or even compostable. 
This is the most expensive nappy option, as inserts are more costly than disposable nappies, however they are usually much better for the environment, and can be a great option when on holiday or away from washing facilities.