If a bookstore buys a book, they now have a book. What they do with it is mostly up to them. They have the right to "sell or otherwise dispose of" the work, according to the first sale doctrine / 17 U.S.C. 109. They do not have the right to copy it.
The Pirate Bay involves one person sending a copy of a file to another person, but that doesn't mean the original copy was destroyed. That lack of destruction is really the foundation of BitTorrent in a way - files are shared among many people. Then, if one person has the file active, it can be downloaded again.
So people who upload a new torrent on TPB are breaking the law in that they're copying something they aren't allowed to copy. People who download and then seed a torrent are illegally obtaining a copyrighted work. The fact they upload it also means they're illegally copying it, as the author has the sole right to copy it.