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?
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.
Does one top up or top off rechargeable batteries?
The answer is probably neither. No doubt by "rechargeable batteries" you mean the small batteries we use in electric toys etc.
We Charge lithium-ion batteries
Note "Big" lithium-ion batteries are normally not fully charged, this is to extend the cycle life of the batteries. Therefore they are not topped off they are just charged.
Industrial devices, such as the EV, typically limit the charge to 85% and discharge to 25%, or 60 percent energy usability, to prolong battery Battery University Group
The expressions actually come from a time when Lead-acid standby storage batteries had to have a whole room to contain them. And I don't mean some smallish cupboard-like room that many office servers are kept in.
Normally a Lead-acid standby storage battery is kept topped off by a float charge which does not damage the battery and maintains it at full charge. However, if the battery is ever called upon "to do its job" the battery charge level will drop. The voltage level a charger should supply in case of charging a discharged battery is higher than that for the float (top off) charge. The battery should be disconnected from the rapid charge voltage, once it is fully charged (Topped up) or it would be damaged.
The comment by MANIKANDANCHELLAKKAN in this article describes charging requirements for Lead-acid standby storage batteries Battery charger