A cover or wrap is used make a nappy waterproof. Not all nappies require a cover, something like an all in one already has a waterproof outer-layer but for other nappies like shaped nappies, or the traditional terry you will need to add a waterproof cover.
Most covers and wraps are made from PUL. You can also get wool covers but I don’t have personal experience of these yet.
Covers and wraps are the same thing, don’t get worried about the different words, I definitely use them interchangeably. In my mind a cover is part of an all in two system whereas a wrap is something that is used over a shaped or flat nappy, but either word is fine!
Covers and wraps are available in popper or velcro fastenings. Some are sized, some are birth to potty. Here are some reviews I’ve done on wraps so far, if you’re after an all in two system then have a look here.