There are a number of different types of modern cloth nappies, and it can be confusing at first. So here is a brief description of each type, and their pros and cons.
Flat nappies provide average absorbency and come in several different styles. Generally they are a square, and made out of terry towelling or brushed cotton (flannelette). They require folding and need to be fastened with pins or a snappi and need a waterproof cover. The main advantage to these nappies, are their low cost and exceptionally fast drying times.
These are like flat nappies however they are generally multiple layers of cotton sewn together, and frequently contain a sewn in panel for extra absorbency where it's needed most. They require minimal folding, but have the same fastening and cover requirements of a flat nappy. They are only a slightly higher cost than flat nappies.
Pocket nappies are shaped to fit the baby, generally with elastic legs and backs, and with snap or Velcro fastening. They have a waterproof outer and hydrophobic (stay dry) inner, forming a pocket that you stuff with an absorbent booster. Pocket nappies can be stuffed with specially designed inserts, but you can also use flats or even old towels you cut up. Having the absorbent bit separate, means that drying time is quite good, and you can adjust the absorbency depending on your babby's needs. These nappies are available in one size which grows, or multiple sizes which can be less bulky, but more expensive.
Fitted nappies are multiple layers of an absorbent material sewn together into a shape which fits around the baby, generally with elastic legs and backs, and with snap or Velcro fastening. You need to use a waterproof cover with these nappies, and they can be slower drying than the pocket nappies. Again, these nappies are available in one size which grows, or multiple sizes which can be less bulky, but more expensive.
All-in-one's are like a fitted nappy with the cover combined. They are shaped to fit the baby like a fitted nappy, and usually close with velcro tabs. A waterproof outer is sewn in and prevents moisture leaking through. They are very easy to put on but have the longest drying time of all the nappy options. Again, these nappies are available in one size which grows, or multiple sizes which can be less bulky, but more expensive.
Covers relate to the outer layer that blocks moisture from escaping the nappy. Covers are available in a variety of different styles and fabrics. They can be in a pull-up-pant style with elasticised legs and waist, or a wrap style which wraps around the nappy and does up with snaps or velcro fastening. They can be made from a material with a PUL leak proof backing, or wool or fleece for extra breath-ability. Covers only need to be changed when they become dirty, hence you only need about 1 cover to every 3 or 4 nappies.