A pocket diaper has an outer layer of waterproof material (usually PUL - polyurethane laminate) and an inner layer of microfleece or suedecloth. There is an opening (usually at the waist) where you slide the insert or absorbant part of the diaper in. Examples are BumGenuis, FuzziBunz, Happy Heinys, Thirsties Duo Diapers
A prefold is a rectangular shaped diaper with 3 'sections' divided by seams. The center section has more layers than the outer sections. This is referred to as ply (i.e. 4x8x4). A prefold can be pinned or simply folded and placed inside a waterproof cover. These are a great choice for newborns - many moms agree! This is your 'grandmothers' diaper. Prefolds combined with covers are the MOST cost effective way to cloth diaper.
A diaper cover or wrap is made of a waterproof layer of material. These are used to cover prefolds, flats, fitted or contour diapers. Diaper covers can have a snap or velcro closure. Covers can be a wrap (fastens at the waist) or pull up type - common with wool and fleece covers.