We often think of "on the clock" employment in terms of shift work, where the worker has a scheduled, fixed-length shift with a single employer, and whether they're actively working during that time or waiting around for the employer to tell them what to do next, they're paid for the hours on the clock.
But it is possible for ridesharing companies to employ workers in "micro-shifts" that last the duration of a single ride.
So, Driver X has two part-time jobs: as a part-time employee of Lyft and a part-time employee of Uber. Driver X is ready to work, so checks the apps, and sees there's a Lyft assignment available. Driver X accepts the ride, and for the duration of that ride, he is working exclusively for Lyft, and Lyft pays him for the time worked. Once that ride ends, his micro-shift with Lyft ends, and he's now available to work for either of his part-time jobs again.
The idea of micro-shifts may seem, at first blush, more like a contractor relationship than an employee relationship. And in the past, gigs that used this model were more likely to involve a contractor relationship -- but they also gave the contractor much more freedom in terms of HOW they accomplished the work.
In contrast, if you look at Uber and Lyft, ignoring the micro-shift aspect, there is very little difference between how those jobs work and how other service-oriented part-time jobs work, in terms of the power the employer has to dictate HOW the work gets done.