A dependent contractor
is an employee (if they are an individual). This has been the actual state of the law for decades in the US and EU. Redefining existing terms doesn't change that, and the parent's comment doesn't create a meaningful distinction between the existing classifications.
Worse, it creates distinctions that are based on factors that are largely irrelevant to the employee-contractor classification.
Today, employees are free to choose to stop working whenever they want (the US has at-will employment) and can work for multiple companies (indeed, most American workers work for multiple companies, especially those who work multiple part-time jobs to make ends meet).
I don't know of any contractor that can choose to stop working for several weeks without notice during a contract and get rehired by the client they walked out on. They'd have to find a new client. This is no different from an employee getting terminated for not showing up for several weeks.
And with respect to getting paid by the job: while this is one of the big factors for independent contractors, it is not exclusive to them. Employees in the entertainment industry get paid per job (game programmers get paid per game, members of the Hollywood guilds and unions get paid per project, union musicians get paid per recording or tour, etc.)