While writing a forum post on proper lithium-ion battery care, I started wondering whether the proper term for recharging them while still fairly full is called topping up or topping off.
Perhaps both are accepted?
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Either one is acceptable.
Both are metaphors from filling containers with liquids -- whatever you may have been taught, electricity is not a liquid, but it often seems to behave in similar ways, and of course there were no native words for electric phenomena until it was discovered, so metaphors are inevitable. (Much the same thing is true of computers, for the same reasons.)
Both are phrasal verbs. One uses the common completive up particle (burn up 'burn completely', fix up 'fix completely').
The other has a usage of off that refers to the fact that open containers of liquids can overflow their top when overfilled -- this is the source of the causative verb to top 'cause (a vessel) to become full (of liquid)' -- plus the off that occurs in run off 'overflow (of liquid)'.
So top up means 'fill completely' and top off means the same thing; both indicate at least a chance of overflow in an open vessel. And which one gets used is largely a matter of personal or occasionally local taste. There's no semantic difference.
When you fill your car with gasoline it is common to "top off" the tank by adding a little more after the pump automatically shuts off. People use the same language when referring to a charge on a battery.