Streaming plays straight away like youtube. Torrents you generally have to download first using bittorrent like software. Though it blurs a bit with software like Popcorn Time.

The Pirate Bay is known for its championing piracy, in general. Those streaming sites are piracy. They also usually use the same source videos as those found on torrent sites; if not outright acting as a thin media player on top of torrents, in some cases.