Musical duo Lexie Jay and Jon Fedorsen had pulled over to check driving directions in downtown Toronto, when two well-dressed strangers opened the hatchback of the band’s SUV and started loading their luggage into the trunk.

Ms. Jay turned around to ask what they were doing, “and they said, with confidence, that they would like to go to the airport,” she recalled. Realizing they must have mistaken their vehicle for a ride-hailing service, Ms. Jay laughed.

The would-be passengers were mortified. “They awkwardly began to extract their oversize bags from the trunk, exclaiming, ‘Sorry, We thought you were our Uber!’” Ms. Jay said.

Ride-hailing vehicles have become ubiquitous in cities around the world, increasing the likelihood of mistaken encounters between prospective passengers and unsuspecting everyday drivers.

Today, Uber counts more than 1.5 million drivers in its global fleet, while Lyft has about 700,000. The drivers, who get connected through a smartphone app to passengers seeking rides, use their personal vehicles to transport those riders.