Flats: Usually made from 1 layer of cotton (also available in hemp and bamboo), they’re easy to clean and dry quickly. They most often come in 2 sizes (infant and toddler) and can be folded a million different ways and then secured on your baby with either a Snappi 
or Pins
. They’re extremely cheap usually. A cover is required to be waterproof.
Prefolds: Prefolds are similar to flats in that they need to be folded and secured on your baby with either a snappi or pins. They’ve got more layers of fabric (cottons, hemp, or bamboo) than flats and come in lots more sizes. The middle section of the prefold is thicker for more absorption. They come in bleached and unbleached versions (cotton). They are easy to clean and dry quickly like flats. A very economical choice! A cover is required to be waterproof.
Contours: Contours are like prefolds but they’re cut into the shape of an hourglass instead of just being a rectangular piece of fabric. There’s no folding required, you just pin or snappi it in place. Some have elastic in the legs and some don’t. Usually made from cotton blends, they’re easy to clean but take a little longer to dry. These are a great option for easily customizing to your babies size (like flats and prefolds too). A cover is required to make it waterproof.
Fitteds: This diaper resembles a more traditional disposable diaper, no folding or snappi/pins required. They come in either snaps or aplix/hook & loop (like velcro) closures and are available in lots of fabric options. You’ll see lots of colors and prints to choose from and they come in different sizes and one-size versions, too. These make fabulous night time diapers. Still pretty easy to clean but tend to take longer to dry compared to the versions listed previously. Needs a cover to be waterproof.
Pockets: These are probably the most popular type of ‘modern cloth diapers’. They’re basically just a waterproof diaper that has a pocket that you can stuff with an insert(s) (in different fabric options) for absorbency. You’ll see both snaps and aplix closures and sized and one-size versions. There are lots of different brands to choose from, some are economical and some being more expensive. Pockets are easy to clean, although microfiber inserts tend to have stink issues over time according to some moms. This style of diaper does dry fast (I typically hang my ‘shells’ to dry and toss inserts in the dryer). You don’t need a cover because the outside of the diaper shell is made from waterproof fabric, usually PUL (polyurethane laminate).
AIO (All In One): This is the cloth diaper option that’s most like a disposable diaper. It’s one piece (the insert is sewn in/attached) and comes in both snap and aplix and sized and one-size versions. You’ll also find a variety of fabrics, colors, and prints available. Easy to use but they tend to be a little harder to get clean and often take quite awhile to dry, this being a common complaint of users. They make great diapers for daycare, babysitters, and grandparents. No cover needed as the outer layer is waterproof (typically PUL).
AI2 (All In Two/2): Similar to pocket diapers, except the absorbent insert lays on top of the diaper instead of inside it. The advantage to this is that (sometimes) you can just change out the insert when it’s wet and put in a new one, while reusing the shell until it gets soiled. Just think of AI2 diapers as a 2 part system if you get confused. These types of diapers can be economical as you can buy fewer shells and more of the less expensive inserts. The shell can then also be used as a cover for prefolds and flats since it’s waterproof.
AI3 (All In Three/3): Exact same thing as an AI2, except the insert/pad itself is a 2 part system. 2 part insert plus the shell/cover equals 3 parts. Typically the 2 part insert is an adjustable option for offering more absorbency as well as quicker drying for cleaning time.
Hybrid: Basically, a diaper that is part disposable and part cloth. Most brands offer a water proof shell with either a disposable (to throw in the trash, compost, or flush) or a regular cloth insert. These make great travel diapers. This is not the most economical diaper if you’re using the disposable inserts all the time, they can get pricey. If you use the cloth inserts, then they’re often referred to as an AI2 diaper. Like an AI2, you can then use the shell as a cover over prefolds, flats or fitteds. As with all the other diapers, you’ll find a variety of prints, fabrics, closures, and sizes.
