Have a look at The Nappy Lady website. Your posts suggested you knew more than you actually do 
All nappies consist of an absorbent bit and a water proof bit, whether washable or chuckable.
All In One - AIO - is like a disposable that you can wash. You have a waterproof (Polyurethane Laminate, either cotton or nylon) outer shell, an absorbent middle (cotton or bamboo terry, microfibre like cleaning cloths or hemp jersey) then a fleece bit that goes next to the baby's skin to wick away moisture. The absorbent middle usually flips out so they dry faster, 3-4 hours on my radiators. They fasten with velcro (or aplix, which is a softer version) or poppers. Less faff than getting to the shops when you've run out, or baby's grumpy/cluster feeding/it's pissing with rain.
The there are Pockets. These are the cheapie ones that you see on ebay in cool prints. You get a waterproof outer and a fleece inner like the AIOs but have to stuff them yourself. Takes me 10 minutes to do all mine or an extra 30 seconds if I've been lazy and haven't prepped, and they offer greater flexibility because the different materials have different absorption rates. Slightly faffy but still easier than getting to the shops.
Two parters are also called fitteds. You get a nappy-shaped bit made of several layers of terry - like a ready folded traditional flat nappy - which you put a waterproof layer over. This can be made of PUL, fleece or wool (which needs lanolising). Fairly faffy, but with the right nappy plus extra layers you can get 10+ hours overnight.
Flat nappies are traditional ones, either the terries which are like a towel or prefolds which are smooth and part-folded then stitched. Mucho faffola but very very cheap. You need a wrap like the two parters for these. You'll also need pins or nappy nippas for these.
Google "nappy library + " and it's likely that you'll find lots of real life people nearby using cloth :)