Torrents download from multiple sources all at the same time. So as you are downloading other people are downloading from you. It literally is a torrent.
P2P sharing is sharing between 2 individuals hence depends on the upload speed of the one doing the sharing.
If a torrent file is popular it will have plenty of "seeds" and will download very swiftly to your computer.
Both methods can be dangerous in terms of virus, trojans etc. I would say Bit Torrent is safer than P2P sharing.
On torrent sits it's a good idea to look at the comments before clicking download as these will warn of malware etc.
Hope this helps, John