It's not quite the same (although they will throttle torrents frequently). Basically some firm gets hired by a media conglomerate to look at a torrent swarm for one of their shows or movies, and log the IP addresses that are sharing the data.

Then they look up the IPs, see that 123.456.78.90 was connected through a Comcast account. They send a big pile of requests to Comcast with all of the Comcast IPs and ask "hey, who had the IP 123.456.78.90 on January 14th, 2016 at 4:50pm?"

Not sure how often they actually bother suing actual users these days but either way, the ISP got the complaint and turns around and sends you a letter saying "hey, stop downloading tv shows and movies over torrents or we will have to cut off your service."

I'm sure the details of how this works change and are more complex but that's the essence. Even if you aren't sued, your ISP will cut you off if you keep torrenting stuff and generating complaints from rights holders.