I think some of the confusion is due to the fact that companies aren't always careful which terms they're using. But to be specific:
Lambskin/sheepskin is the actual skin of the sheep with the fleece attached.
Fleece is the sheep's woolly covering. It's very springy and dense.
Wool is the fleece spun and manufactured into thread or yarn and then into blankets or clothing or the like.
That's how I understand it at least. But I think you can sometimes find things labeled "sheepskin" (such as a jacket) that doesn't actually have animal skin, or for instance, when we talk about "fleece blankets" for babies, they're usually polyester, I think named because they have some of the water-wicking abilities of real fleece.
For mattress covers, we love our SnugFleece:http://www.snugfleece.com/
It's fleece, so it's the wool shaved off and attached to a backing -- no killing the sheep. It's really cushy and nice, and they have a bunch of sizes, including crib. The elastic corner straps make it stay on well, though it can shift a little (but my DH is a really shifty sleeper!). We used to have a synthetic mattress cover, and I will never go back -- sweat city! It would block the sweat from getting through, so it would just pool and yuckify the sheets.
This wool cover is nice in the summer and winter both. I feel nice and dry, and the mattress so far is fine. Caring for the cover's easy, too -- just let it air out once in awhile without the sheets on top.
I'll stop trying to sell you a SnugFleece.
I found mine on eBay for cheaper than usual, but I'll tell you that they're worth full price if that's all you can find.