Theft removes an item and make it his. Copyright infringement is copying someone’s item, reproduce it and make money out of it. File sharing is duplicating a file, which the owner can still have the original copy, and share it among the people. Piracy is stealing or robbing on the water.

I took a slightly different, simpler, angle:
http://www.blackgate.net/blog/index.php/sharing-is-not-piracy/
http://www.blackgate.net/blog/index.php/copying-is-not-piracy/