In private and sometimes in public, Travis Kalanick was fond of describing Uber, the car-hailing service he co-founded and commanded absolutely, as the Amazon of the transportation business.

The similarities were clear. Amazon began as an online bookstore, but it was never just about selling books; over two decades, Amazon’s founder, Jeff Bezos, methodically expanded his company’s range, operational infrastructure and ambitions to ultimately pose an existential threat to the entire retail industry.

Uber, in Mr. Kalanick’s expansive vision, was similarly never just about hailing rides. To him, a taxi-like car service has always been a gateway for a business model that he believed would upend the entire trillion-dollar global transportation industry, altering the way people and things move around the world — and turning Uber into one of the handful of American tech giants that will lord over this century.

That vision now lies in the hands of Dara Khosrowshahi, the longtime chief executive of the online travel company Expedia, whom Uber on Sunday picked to replace Mr. Kalanick. Mr. Khosrowshahi faces one primary question in that role that has everything to do with ambition: Will the company still aim to become the Amazon of transportation, or will it settle for being the Expedia of its market — one of the largest of several players in its industry, but not expansionist and messianic, hellbent on becoming the next great American technology behemoth?