Definitely unique. I've never lived in DC but visited a few times for work and was flabbergasted when I heard about slug lines (I still am). It's a bad driving situation when you'll voluntarily get into a stranger's car, and drivers will just let random strangers in their car. That doesn't happen in any of the cities I've lived in.
They do this in the SF Bay area, it's called casual carpool. Very popular in the East Bay. I used to do it for many years, both as a driver and passenger. It's all about getting past the Bay Bridge toll plaza, and the carpool lane goes way faster than the (sometimes horribly) backed up traffic. The FastTrac lanes aren't any good when it gets so backed up.
Yes there are myriad unspoken rules, and hilarious stories about when they are flagrantly violated. But over the years I've had some great rides, met some wonderful people, discovered some new music, and generally enjoyed the experience of intermixing with fellow humanity in a random but mutually beneficial way.
An acquaintance I know has been going to work via a slug line for more than 10 years. It's impressive that it is reliable enough for getting to a day job. There are even unwritten rules you're supposed to follow and so on when in someone else's car.
Now I guess with Lyft and Uber it might seem less strange being in someone else's car these days. But before I can see how it would look totally weird for someone from out of town.