nospam
a battery charger does just that, charge batteries, usually removing the battery from the device and inserting them into the charger.

that's different than a power supply, which powers the device and which may also charge a battery while the battery is still in the device.

Tony Cooper
Wait a minute! You've said in another post that people call them different things, and that's OK. So if that's OK, then calling the power adapter a "battery charger" is perfectly legitimate by your rules. If it's used to charge the battery, calling it a "battery charger" is logical.

Sandman
It's not a battery charger, regardless of what people call it.

The USB brick is a power adaptor. It takes the power from your wall socket as input and provides a 5 or 10 volt output to the device. This is not a power supply unit either.

The battery is not a PSU either, the PMIC (power management integrated circuit) chip in the iPad is a the PSU. It takes the power from either the battery *or* the power adapter and provides electrical current to the load (i.e. the iPad).

Wall Socket ->Adapter ->Lightning port ->PMIC ->Motherboard Battery ->PMIC ->Motherboard

Few would call a PMIC a PSU, but it's as close as a PSU you could get to in a mobile device. It's the chip that takes the input power from an energy source (wall socket, battery) and delivers it through a power output to the load.