I think there are two differences: urgency and immediacy. A checklist is urgent in a way a to-do list isn't. The sky will fall if a checklist is not followed when X happens, whereas a to-do list is kind of a nebulous list of nondescript tasks. A checklist's immediacy also implies a strict ordering, whereas a to-do list does not. For example, task A must be completed before task B or the sky will fall.

It's just a lot stricter operationally, which is why I think you'd get a lot of pushback trying to implement one for non-critical business tasks.