Conceptually, a taxi is a regulated industry. The regulation created by the government sets the work conditions, and the taxi medallion is the contract between the taxi provider and the government. In a way, it's different from both the contractor and employee status which is usually between 2 private parties.

The owner/recipient of the medallion agrees to certain work conditions/obligations (non-discrimination, destination-blindness, accept credit cards, sometimes provide wheelchair amenities, etc.) and receives certain privileges (limited monopoly, right to pick up anyone on the street, right to use taxi lanes and taxi files, etc.). Whether the drivers actually meet the obligations is often a matter of lack of enforcement and what the driver can get away with, but it really is a quid-pro-quo of rights and responsibilities.

Medallions ended up being owned by taxi companies who rented them out to contractors or employees, so the relationship between the medallion owner and the driver (2 private parties) depended on how they set up the contract (and both kinds exist). And of course, private parties abuse independent contractors and employment contracts all the time, so it's really a gray area in practice. But regardless of who is paying whom, the driver should adhere to the medallion rules while driving/waiting on fares.

When looking at taxi and ride sharing, it helps to have a brief history of the industry:

- Before medallions, anyone could call themselves a driver, and pick up anyone for any price--true market competition. Of course, abuse and discrimination was rampant, riders were vulnerable, and too many drivers would drive the offered price so low only the desperate in dilapidated/dangerous vehicles would compete.

- Regulation in the form of medallions and meters came along with the idea of promoting mobility. Limit the number of drivers and set the fares so that someone working full-time can make a decent living, make sure they have safe vehicles and not criminal drivers, mandate shortest routes and non-discrimination. In the best of all worlds, there is a competent fleet of drivers, and people can get around the city and suburbs as needed.

- Because this is not the best of all worlds, taxis became sleazy and abusive, the medallion owners exploited their drivers (both employees or contractors), and regulatory capture ensured that the customer protection obligations were no longer enforced.

- Uber and others exploited the loophole of the radio-taxi: you phone in and get a taxi dispatched to your location. Except with mobile phones, that's like standing on the curb and hailing a taxi, which was the artificial monopoly given to taxi medallions. Frankly, I think ride-hailing apps should've been regulated on that alone, but because the whole industry had such a bad reputation and entrenched interests, everyone was happy to find a way around them.

- As the middle-men, the ride-hailing companies are trying to set themselves up to get the best of both worlds: set prices and make sure drivers aren't really free, but also not have any of the responsibilities of keeping ride-for-hire on the road or promoting mobility.

Another side of this whole contractor/employee debate is the destination-blindness. As a driver, you don't want to drive the unprofitable fares, either too short or too long to the suburbs without a return fare. In order to be appealing to riders, Uber et al. have to hide this from the drivers, otherwise the drivers would refuse more rides. If all drivers became true contractors free to set rates and pick-and-choose any ride, we'd be back to the original unregulated situation (race to the bottom). So the companies get why the regulations exist, but if the drivers were employees, then the companies would have to bear the cost of the unprofitable fares. So they make the drivers feel like contractors to bear that cost for them.