[Grammar] on or off battery

Hello, everyone! Do portable electric devices (radio, cell phone, laptop etc) run on battery or off battery? I've come across both forms and just curious which one is right or preferred. Thanks in advance!
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Feel free to correct my sentences. I welcome them, not resent them!

Portable electronic devices (radios, cell phones, laptops, etc.) run on batteries.

RonBee said:

Portable electronic devices (radios, cell phones, laptops, etc.) run on batteries.

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By the same token, some devices that are usually run off the mains supply can be run off a battery.

They run off or run on until they run out.

In the context of batteries, you can say "run on", "run off" or "run from". The meaning is clear so it's down to personal preference and, probably, local dialect variations.

In the context of mains electricity you can say "run off the mains" or "run on/off mains power" or "run from the mains".

I'm not 100% certain, but there might be a difference between AmE ("run on betteries") and either BrE or AuE ("run off betteries").

To me, run off a battery could suggest that the device is connected to an external battery.

Tdol said:

To me, run off a battery could suggest that the device is connected to an external battery.

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Yes, that's what it means to me too. That's what I intended it to mean when I mentioned it. A device runs on batteries, but if you have the right connection, you can also run it off a car battery.
It doesn't run 'off' batteries, and you (generally) don't run it 'on' a car battery.