The AA branded unit is a smart charger and should not be described by them as it is on the box as a trickle charger.
It can be used for keeping the car battery charged while the battery is connected to the car due to its microprocessor control and its very stable DC electical output.
Trickle chargers were inexpensive, badly regulated low current DC output chargers and the AC spikes that were present due to poor mains regulation that can be present on their output can damage alternator diodes.
Therefore with a proper trickle charger, you cannot condition the battery by having the trickle charger connected to the battery while the battery is connected to the car as it can damage the alternator.
A bad product description but may other vendors also mis describe battery chargers.