Thank you. I think there is more in it, though. When you only talk about ability to pause, you still don't change the sequence of execution - you only can inspect it at arbitrary moments. The sequence itself remains immutable. It's not so clear when you use continuations themselves within that sequence. Say, you save current continuation as an object in memory and then return to it - not immediately but after some other actions are done. In this case you have more questions about how perfect is your return to the state when that continuation was saved is. Indeed a perfect return would mean the whole memory state of the machine is restored exactly as it was when the continuation was taken, and, barring side effects, the execution will repeat what was done after the continuation was taken but before it was returned to.

I'd like to hear more about control flow state and data flow state here.