Correct me if Im wrong but I think the main difference is the use of a tracker in bittorrent.In peer-to-peer sharing, you use a software program to locate computers that have the file you want(I used kazaa long time ago)To locate the file, the software queries other computers that are connected to the Internet and running the file-sharing software.The file-transfer load is distributed between the computers exchanging files, but file searches and transfers from your computer to others can cause bottlenecks and some people download files and immediately disconnect without allowing others to obtain files from their system.
BitTorrent client software communicates with a tracker to find other computers running BitTorrent that have the complete file (seed computers) and those with a portion of the file ,the tracker helps the client software trade pieces of the file you want with other computers in the swarm. Your computer receives multiple pieces of the file simultaneously.I hope this help you.