You probably know most of this -
Braided elastic has fibres wrapped around cords or ribs of the stretch fibre. The strands of stretch stuff are 'braided' into a strip.
It has distinctive parallel, lengthwise ribs and when stretched it loses it's shape and narrows across the width. It loses it's shape and stretch retention when stitched through so is best used in casings, whether on waists, sleeve/leg edges. Often it's described as 8cord (braided) elastic, 12 cord (braided) etc. as well as braided elastic.
Cord elastic - Braided elastic cord is a round cord of elastic (one thick strand of stretch stuff or several thin strands ) covered with a braided (plaited) thin sheath. For examples, think of thick or thin bungee cords, round covered stretch cords, round hat elastic, etc.
Knitted elastic is made by knitting an elasticated yarn (fibre wrapped around stretchy stuff). It's possibly the quickest type of flat elastic to manufacture and has less 'stretchy' stuff in it than other forms of elastic because some of it's stretch comes from the knitted construction. The stretchy stuff is more about recovery of the knitting if that makes sense. It's usually quite soft, strong and lightweight. I doesn't narrow when stretched and because of it's knit construction needle piercing doesn't alter it's shape so it's ideal for clothing in casements or directly stitched on.
Woven elastic is strong and is often thicker than other elastic types. It has a crisscross windowpane look because it has both crosswise and lengthwise ribs. It stands up well to needle piercing which does not weaken it and it does not narrow when stretched. It comes in a wide range of weights/sizes. The lightweight types can be used on clothing and the thicker heavier woven elastics are used for home dec, bags, accessories, upholstery, car upholstery and other heavy duty applications.
Clear elastic is usually a transparent polyurethane. It's a synthetic product and tends to be used for specialist applications. It's very stretchy, recovers well but care has to be taken when applying it with stitching to keep needle penetrations to the minimum.
You can buy 6mm wide elastic in
woven,
knitted,
braided and
clear (the
links are examples only not recommendations)
The quality, life and recovery of elastics is related to what it's made of and the amount of the 'stretchy' product in it, which is usually rubber/latex or synthetic rubber. For elastics in leotards, dancewear, activewear, etc. it's recommended to choose better/best quality over cheapness.