Pocket diapers have a waterproof outer layer, an inside layer of fabric that keeps the skin dry, and those layers make a pocket where an absorbent insert can be placed. An example of a pocket diaper is Fuzzibuns
All-in-One diapers (AIO) are the easiest to use. These are often called 'daddy friendly' or 'babysitter friendly' diapers. There aren't multiple pieces, the outer layer waterproof cover is attached to the cotton or fleece on the inside. An example of an AIO diaper is the Bumgenius AIOs.
Photos from http://www.bumgenius.com
a Diaper Cover is a waterproof outside layer that you can use over flats, prefolds, or fitteds. These can come in all different colors, prints, and sizes with velcro or snap closure. An example of a cover is the Flip cover. It's a one-sized cover and can fit 10lbs-40lbs.
Photos from http://www.flipdiapers.com/flipcover.php
Fitteds are a type of cloth diaper that need to have a cover. They are made from all different types of materials from bamboo to cotton fleece. Fitteds are (from what I've experienced) the most absorbent. Some are made with snaps and velcro while some are made to be closed with snappi's. Some examples of fitteds are Goodmama's, Thirsties Duo Fab Fitteds, and Kissaluvs.
|Thirsties Duo Fab Fitteds|
A Stay Dry Insert like the Flip insert is made to go inside of a diaper cover. The Flip insert is a one sized insert that can be folded to adjust to the size you need.
photo from kellyscloset.com/
A Prefold is what some might consider 'old fashioned' cloth diapers. They are rectangle shaped layered pieces of cloth that can be folded multiple different ways and placed in to the diaper cover. Cotton, Hemp, and Bamboo are the most used materials for prefolds. These are the most economical cloth diaper option if one of the reasons you are looking to cloth diaper is to be more economically savvy.