I get a little mentally disjointed (OK, a little MORE) in 'things to protect your electronic device' discussions. I think most (but not all) people mean this:
Cover = A flat, folded sheet with two flaps and a closure that looks kind of like a book cover and protects the front and back, but not the edge of your device. Usually flexible, like a magazine's covers. Often made of flexible leather or leather-like plastic.
Sleeve = A closed-ended pouch with one edge open that you slip your device in to protect all but the one exposed edge. Some have zippers and other closures to protect that edge as well. Some are stiffer material, some merely padded. Some have one stiff face, with an insert to protect the screen against pointy things.
Case = A fully closed enclosure, usually zippered on 3 sides, made of stiff, strong material to protect the device from any direction, even from pointy things. Usually aluminum or hard plastic.
Is this the most common nomenclature?
Personally, I use cases, but not covers. I have sometimes used sleeves, if one came with the device. I still think $10 Casio calculators have the best system, with the little reversible lid you can slide off the front and slide on the back, but no eReader offers them, AFAIK. I haven't even seen any on the aftermarket. God knows what we'd call them.
