No - oscillators need constant energy input in order to operate. Time crystals require no energy for temporal repetition.
That's not really right. You can oscillate without constant energy input. Two particles can orbit forever.
But normally that oscillation represents stored energy.
They key to a time crystal is that it's oscillating while it's in a minimum energy state. It would take energy to make it stop moving.
A pendulum in a vacuum will oscillate forever, requiring energy to stop. Is it like that?
It requires force to stop. But you can output energy as you do so. Not so with these. They have 'no' energy despite movement.
Don't quantum harmonic oscillators oscillate even in their ground state? How is a time crystal different from a garden-variety QHO?
Nope. Like in the ground state of the hydrogen atom, the ground state of the quantum harmonic oscillator has the wave function spread out in a sphere, and this wave function stays constant in time. Almost all quantum systems do something like this in the ground state, which shows why the time crystal is something new and interesting.