Name-dropping fallacies doesn't make your position make any more sense. Create a third option and someone will ask why there's no option between 2 and 3. Create a fourth option and someone will ask why there's no option between 3 and 4. It's non-central fallacies all the way down, until there are no categories for anything at all, because each and every single person occupies their own category, reductio ad absurdum.

So I posit that we have separate categories for very clear and simple historical reasons: we have "employees" because a set of laws came into being to push back against employer abuses, and to improve conditions for workers generally. "Employees" are not "slaves," is the primary distinction there.

But if I own a company and hire another company to provide services, I'm not hiring an employee, I'm establishing a contract, so a different set of laws comes into play to attempt to ensure fair dealing. But what if the "company" I hire to provide services is a single-person company? Is that just a fiction I'm employing to get around those laws that protect workers? Could be, so the courts have established a series of ways to determine the difference.

A contractor, for example, usually provides services to more than one company. I've done this as a software developer. So Uber might claim that because drivers can work for Uber or Lyft or other ride-sharing services, that makes their drivers contractors. Drivers claim that doing this results in serious disadvantages compared to drivers who exclusively stay with one company, so it doesn't really feel like a choice they can make.

A contractor usually has control over their own hours. If I hire a cleaning company to clean my office, I can't really tell them that they have to come at exactly 2am and work until exactly 3:30am; I give them my business hours and ask them to work outside of those. They have other offices they clean, so they choose the hours they allot to each. Uber, again, might claim that drivers can sign on or off as they will, but there is a very strong effect that has on ratings and compensation, so drivers have claimed it doesn't really seem like a choice, but a requirement.

Again, the reason for this distinction, historically, is to protect workers from mistreatment by employers while still providing the freedom to workers to have more than one client, control their own hours, etc.

The debate here is over whether gig workers really control their own hours, really work independently, really have the benefits of being contractors, or whether that's a legal fiction used by companies to avoid treating their workers well.

If there's a need for a third category, what would be the point of that? Would this third category result in workers being treated better than they are now as contractors? What advantage for employers would there be over treating workers as contractors? The general argument from the companies to date seems to be reasonably summarized as "our business model doesn't support treating our employees as employees," which is not an argument that anyone should actually care about. If there are good arguments why people who drive full-time for Uber should not be treated as full-time employees, with all of the benefits associated with that, Uber has failed to make a good case for this in court to date.