AH is the most important factor for deep cycle batteries.
It's used almost exclusively when talking about off-grid and battery backup systems, solar, wind, battery banks, inverters, etc.
In charging, the size of the battery (or bank) determines the max rate to charge.
Older chargers used to be undersized to prevent battery damage, so the max limit was approximately C/10.
So a 100 AH battery should not be charged at a rate any greater than 10A. High rates of charge on a full or nearly full battery causes the electrolyte to boil and produces sulfation.
Smart chargers monitor voltage, current, and sometimes battery temperature, and have ideal charge curves in their memories, so they can prevent damage through monitoring and adjusting the charge profile better than the analog limited older charges that used voltage only. The smart chargers "Dump" charge into a discharged battery until the voltage rises to a certain point and then start throttling the current back. The smart chargers also charge the batteries "more fully", because they tailor the charge profile to the battery and switch to high voltage low current when the battery is almost full to prevent damage.
So the newer chargers are sized to C/5 maximum, with a recommendation to remain around the C/10 range for maximum battery life.
So at C5, a 100 AH battery could be charged with up to 20A without much damage.
The more deeply discharged batteries have a higher "acceptance rate" and can tolerate higher initial charging rates. Even up to 25% of their AH capacities. That is also affected by type of battery. AGM batteries have acceptance rates of nearly 100% of their capacities.
The C/10-C/12 limit also on the chargers themselves.
If they charge battery banks over their C/10 rates, they will be supplying their maximum current for longer than designed and the charger is subject to overheating and damage.
So the 20A charger above shouldn't be used on a bank larger than ~200 - 240AH.