As far as I know, it goes like this:
The device is on standby, or is sleeping, when you've hit the lock/power button on top and the screen turns off, but the device is actually still on. Everything running on the device at this point is, "paused."
It's idling when the screen is still on and the device is actively doing things, but you aren't doing anything with it.
I might be wrong. In which case, someone please correct me.