Here are the basics based on my research. If you have anything to add, please feel free to comment:
Flats: A large square of woven material, most commonly cotton, that have to be folded and pinned. They will leak unless you also use a waterproof diaper wrap/cover.
Prefolds: A rectangle of cotton or other woven material with a thicker, absorbent middle section. Most moms have a few of these around even if they don't cloth diaper because they make excellent burp cloths. They still require a little folding to get the best fit for your baby, but nowhere near as much as flats. Like flats, they'll need pinned and a leak-proof cover.
|Prefold diaper from The Eli Monster|
Fitteds: Fitteds are made from an absorbent material and shaped to fit without folding. They usually close with Velcro or snaps, so you don't need pins. They do not have a waterproof layer, so you'll need a cover to make them leak-proof.
|Fitted diaper "Road Map" by Hen and Chick Cloth|
|Daisy Dots AIO from Hen and Chick Cloth|
All in twos (AI2): Similar to all-in-ones, except that a separate absorbent layer is placed inside of the diaper. This helps them dry faster because each layer is thinner. You can also customize the absorbency by adding layers as needed. They close with Velcro or snaps.
|Custom print AI2 from The Eli Monster|
Pockets: Essentially a specific type of AI2. With pockets, the absorbent layer (insert) is placed in a pocket between a waterproof outer layer and an inner layer of fleece or some other material that lets wetness through to the insert and keeps baby's skin dry. They close with Velcro or snaps.
|Rockin' Broncos Pocket diaper by Hen and Chick Cloth|
One size (OS): Means that the size of the diaper can be adjusted to fit most babies from infancy to toddlerhood as opposed to sized diapers that fit a weight range.
Thank you to The Eli Monster and Hen and Chick Cloth for allowing me to use their product images for this post. Be sure to visit their shops for a variety of cloth diapers as well as other products for mom and baby. To visit the specific product pages seen here, please click on the caption below the picture.