[munificent]

I think the difference is that an oscillator requires a continual driving force to stay periodic. Stop applying energy and it winds down. A time crystal, once it gets going maintains its periodicity.

Mapping it to spatial terms, I think: You could take a bag of beans and lay them out in a nice repeating grid pattern if you want, giving them spatial symmetry. But you have to keep making the grid yourself. The "bean crystal" does not naturally spread on its own. When a real crystal cools, the entire substance aligns into a regular repeating pattern on its own without any external force needed.