She went outside and 'hailed a taxi'. [=waved or called for a taxi to pull over and stop]
The pilot 'taxied' the plane out to the runway.
We caught/took/got a 'taxi' to the restaurant.
(..) - Sascha, call a cab. - We'll get your coat. - Take your hands off! You're going home. You've had too much to drink. Hey, taxi! Who do you think you are, pushing me? What a fool I was to fall for you. - Go with her. Be sure she gets home. (..)1942 Casablanca