Isn't the difference here that a contractor "could" have multiple clients. The fact that some might opt not to do that doesn't seem to have a significant impact on how they should be classified.
It's not the only factor but it is one. I guess it ultimately depends on the country / state / court.
Others factors generally include things like how you get paid (do you bill the client, or are you on payroll?) or the nature of your work (projects and deliverables, or day-to-day operations, etc).
Of course many of these things favour classifying Uber drivers as contractors, but there's enough of a gray zone for a court to rule they are full-time employees.
