More, hopefully clarifying, information:
The blue links at the top left are not the area you are in. They are menus/link to other areas of functions.
So, when you are in the Library, you see a link so you can go to the Store, and vice versa.
The Collections button lets you see the default collections: Books, Purchased Books, and PDF's.
Books shows all the books currently on your iPad: if they have not been moved to another collection. I'll say more about this in a moment.
Purchased Books shows all the books you've ever purchased from the iBooks store, whether they are currently on the iPad or not. If they are not on the iPad, they will have a cloud icon next to them. You can download them by tapping on that icon. The Purchased Books category can be turned off by going to Settings > iBooks and turning off Show All Purchases.
PDF's show all PDF files that have been copied to iBooks. There are several methods to do this. Again, they will not be here if they have been moved to another Collection.
You can create your own Collections by using the + New Collection button in the list. Once created, you tap the Edit button while in Library view, then select and Move the books to the new collection. With the exception of the Purchased Books collection, books can only belong to one collection.
With the exception of the default collections, you can re-order your collections by tapping the Edit button (while viewing the list) and then using the lines icon to the right to drag them up or down.
_Hmm, got carried away and typed more than I intended._
