AA and AAA are literally the sizes. That it.
The volume and shape is the only difference. To get a DIFFERENT battery you would have to go to a different chemistry. Like lithium, or lead acid. And those have their own sizes.
Lead acid has the “Group size” standard because virtually all consumer facing uses are groups of cells in series to get standard voltages like 12v for a car. Their sizes usually determine runtime and how hard it can burst. (Without getting into differences like deep cycle, marine, sli, etc)
Lithium usually has a dimension system, like 18650 (18mm diameter, 65.0mm long) for vape and flashlights. Or xSxP for pouch type cells (RC cars, etc) which denotes how many cells in series and how many in parallel. Starts getting technical here so I’ll stop until more is requested.
Alkaline cells just use an alphabet system for sizes; “AA” “AAA” “C” and “D” being the most common for the consumer.
BONUS: 9v batteries are just 6 “AAAA” batteries in series inside a can.
The only difference between an AA and AAA battery is the size – because the AA battery is larger, it holds more of the chemistry that makes a battery work. The more chemistry it contains, the more power it stores and the longer the battery will last in use before it runs out.
A C or D cell battery is also exactly the same as an AA cell, just even bigger, and while pretty rare, you can get things like AAAA batteries that are even smaller versions of a AAA (these are often found making up 9v batteries – 6no 1.5v AAAA batteries wired in series to make one larger 9v battery).
Not all batteries are the same though – if you look at a CR2 or CR123 battery for example, these use different designs and chemistries to produce different voltages suitable for other uses.
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