the word taxi comes from the Greek word taxithi (ταξίδι) which means travel? And taxi being the means of travel. And that when you call a cab, you are calling a cabriolet? A term which originated from a carriage cabriolet, i.e. a light, two-wheeled, one-horse carriage with a folding top, capable of seating two persons.
Taxi is a very universal word with only slight variations so it is easily recognizable wherever you are in the world. So that’s a good thing. But it’s not always easy to hail a cab. Here’s a video on how to do that in New York City: