A cover is what you put your Kindle in to hold it. The Kindle comes with one. Some people find that it doesn't hold the Kindle in securely so they purchase a new one. I bought a medge cover in red. I will be buying the tree of life cover from Oberon Design next.
A case is something you put your Kindle in with or without your cover. You can find a really good one from Waterfield design. It added protection for your Kindle.
A skin is like a sticker that you put on your Kindle. I like it because it protect
my Kindle from dirty fingers, smudges, etc.. It also brighten up my Kindle. Some people find it distracting. It's a personal preference. You can look at the many designs at Decalgirl.
I find that case and cover are often used interchangeably, although I do agree with Pauline that technically a cover is like a book cover, that you would put your Kindle in to use while reading, and a case would be like a box that holds the Kindle for transport or storage. Also, skins aren't like stickers, more like the static clingy things that you can put on windows. There is no sticky goo involved.
Which of these you decide to use is a personal choice. Some people have all three, even different ones to change out as the mood strikes. Some people even use their Kindle nekkid, which I think is a little freaky It's whatever combination of style and comfort/protection you're comfortable with.
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