LeeAnne --

Library bindings are always hardback, since the purpose is to make the book extra sturdy. They're usually very plain, no frills bindings. Here's the Wikipedia explanation:

Library binding is a way to increase the life of books and periodicals used in libraries. This is done by sewing the pages in place and by reinforcing the spine for each volume. The goal of library binding is long-term preservation. However, library bound books also benefit library patrons because they ensure that the volume in hand is complete, as well as to make the volumes easier to open and photocopy. 

GrannyGamer

LeAnne - I think what you have with your paperback is just something libraries put on covers to reinforce them and keep them intact since they go through so many hands.  Either way, ex library books ARE postable!

LeeAnne, you have a book that a library covered.  That's not the same as library binding, though.  Library binding is a very sturdy type of hardcover binding.  Think about your old textbooks (try to anyway, ha ha!) and it might help you get the idea.

LeeAnne, "library binding" involves taking off the original cover altogether and re-covering the book with a different binding (they're usually either plain colors or some sort of geometric or paisley pattern, almost like some types of wallpaper). They used to be pretty standard till ?the 70s - all the hardback books of my childhood had these - as a means to extend the life of books; these days you don't see that with new books, but if you poke around in the stacks of a big library and look at some old classics, you'll probably see the sort of thing I mean. But if you have a book that has a regular cover - with an illustration, the name of the book and author, etc. - even with some sort of plastic over it, that's not a library binding.