Covers do not have a stay dry lining or any built in absorbancy. Covers can be used over a cloth diaper or diaper insert. Diaper covers are commonly made from polyurathane laminate, wool, fleece or nylon. Wool & Fleece covers are commonly called 'soakers.'
The "Plastic Pants" used in the 60's-80's are a type of pull on vinyl called PEVA (polyethylene vinyl acetate) Gerber still makes them today.
Covers can be pull-on, have snap, or hook & loop tape.
Pockets (or Sleeve) Diapers have a stay dry lining or but no built in absorbancy. Pockets can be used over a cloth diaper or with a diaper insert that is placed inside of a pocket or sleeve.
The Outer layer of a Pocket Daper is commonly made from polyurathane laminate (PUL/TPU) or nylon (Ultrex) or PEVA.
The inside of the diaper (the pocket or sleeve) is lined with a stay dry fabric: suede cloth, fleece, microfleece , athletic wicking fabric are a few examples.
Pocket diapers can have snap or hook & loop tape closures
AI2 and Hybrids
Hybrid or All in Two systems have a cloth outer shell (or diaper cover) and have inserts. Hybrid inserts are usually disposable while AI2 inserts are usually washable, but these terms are used interchanably and care should be made when making a purchase to be sure that you are getting what you expect.
Inserts often snap into place but can also be tucked. AI2 or Hybrid diapers can have snap or hook & loop tape closures
All in One Diapers have built in absorbancy with a stay dry outershell. They are most similar to disposables. A booster can be added to an AIO to add absorbancy for heavy wetters. AIO diapers can have snap or hook & loop tape closures
"Sposies" are made with Sodium Polyacrylate (SAP)
SAP is used in virtually all disposable diaper brands. Brands that replace SAP with plant based starches and cotton exist be are hard to find.
Most disposable diapers use either an adhesive tape or a modified hook & loop closure.