Tlogmer makes a good point. Now for some semantic nitpicking:
The difference between downloading an MP3 from Gnutella and checking out a book from a library is that when you check out a book you are not making a copy of the material. The book was paid for by the library, and then you borrow it for a short period of time. If you were to photocopy pages from the book (for purposes outside the grey area that is Fair Use), then you would clearly be violating copyright law. If you decided never to return the book, that would be theft.
When you download an MP3, you are essentially "Xeroxing" the music. The person who originally ripped the CD still has that CD, or just made a copy of it and returned it. The copyright holder did not receive any money the copy in your posession. However, if the person you downloaded the music from deleted his copy, and the person he got it from deleted his, and so on until the original media was destroyed, then one could argue that this was perfectly legal. It would be like purchasing a used CD.
File sharing is not theft. To quote Webster 1913:
To constitute theft there must be a taking without the owner's consent, and it must be unlawful or felonious; every part of the property stolen must be removed, however slightly, from its former position; and it must be, at least momentarily, in the complete possession of the thief. See Larceny, and the Note under Robbery.
In the context of file sharing, "theft" would imply that the original copy of the song had been destroyed. The word "piracy" also implies this. The clearest description is "copyright infringement." It's not the same as theft.