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You aren't timesharing your tiny mainframe, so it is quite different, yes. The cloud is precisely what your mom had on a mainframe 50 years ago, including virtualization, on-the-fly scaling of resources (maybe a little more difficult because of the larger equipment), and even renting time on computers you didn't have in your offices, since not every institution could afford their own computer.

Both statements are correct. Remember that it was a personal computing 'revolution'. It would be a great step backwards to accede power to cloud service providers.

Computing at the whim of others aka timesharing.

Smile and nod but your mother has seen a few cycles of the industry.

Providing an employee with equipment (such as a laptop personal computer) to do their job is (legally) different than leasing equipment to a contractor, or transfer-pricing between departments in a corporation.

Remember that a timeshare was very expensive and that those costs were accounted for carefully not only for the purposes of internal billing but also for benefit-analysis.