> taxi services in the US have yet to roll out any type of [app] for hailing rides afaik and have a fleet of vehicles with their own livery.

Don't NYC taxis have one? I vaguely recall there being something when I visited several years ago.

[note, I had to guess to fill in the blank for your comment, since it seemed like you dropped a critical word].

One of my local taxi companies (Central Oregon) has an uber-like app for their cabs. So they are changing.

What do you call an actual ride sharing service then?

In Austin, Yellow Cab became Z-Trip, with more of a ride hailing model than the old taxi model. They are cheaper than Uber or Lyft and considerably more reliable. Uber/Lyft will cancel a pick-up (sometimes, without telling you) when the pick-up is less profitable or would cause the driver to leave an area with more ride pickups. Z-Trip has never done that, that I know of. U/L also tend to have more drivers who are less proficient with English, which causes communication issues. Lastly, if you have a medical condition and it's not an urgent trip, Z-Trip can usually handle it. I have had Uber and Lyft drivers cancel on me, once while I was sitting in the car. But the main difference is on price - Z-Trip does not do the annoying surge pricing like the others do.

We call them cabs in NYC for what it's worth