To me, the distinction comes down to: carpooling implies some kind of repeated/scheduled vehicle sharing (like coworkers coordinating a route to get to work at 9a every weekday, while ridesharing is much more ad-hoc/on-demand (like craigslist rideshares between Seattle and Portland to split the gas bill).

Definitely agree that Lyft/Uber aren’t really ride sharing in that sense though — the driver’s goal is to earn a fare on a trip he wasn’t going to take otherwise, while the original ride shares were a cost-reduction on a trip the driver was going to make anyway.