I get that, for a house/solar battery, it sort of makes sense as your typical energy usage would be measured in kWh on your bills. For the smaller devices, though, the chargers are usually rated in watts (especially if it’s USB-C), so why are the batteries specified in amp hours by the manufacturers?
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The main reason is that small batteries cannot give out amperes worth of current. The flow is generally in 10s of milliamps (the draw the device will need). Bigger batteries, like a car battery, have to give out a few Amps at max need (to start the car is about the biggest current draw). So, the capacity of the battery is discussed at the scale it is used for. It “could” be discussed using decimals instead (0.001 Amp versus 1 milliamp) but we tend to want numbers bigger than 1 rather than decimals. Just easier for average person to imagine 1000 of something than it is to imagine 0.001 of something, or the reverse, 10 of something is easier to deal with than 1,000,000.
This is the same idea behind someone saying “x million gallons is equal to 1000 olympic swimming pools” (whatever the conversion would be, I don’t want to look it up) when talking about the water flowing over a waterfall, as an example.
We “could” give the 3200 mAh battery as 0.0032 kAh, or 3.2 Ah, but people like 3200 better than 0.0032 when doing calcs in their heads. The device draws 30 mAmps per hour and has a 3200 mAh capacity, so we can get about 100 hours of use from it. Way better than doing “the thing has a draw of 0.03 amps and has a 3.2 Ah capacity so I can get about 100 hours of use from it”.
With chargers, you may have noticed that the time to recharge a battery is way less than the time of use that same battery generally gives. This is because the charger gives way more current than the battery is required to give when in use. So, it is “appropriate” (useful) to talk about a 3 amp charger, which would need a couple-few hours to charge that same 3200 mAh battery (because it does not give 3 amps the entire time of charging, just when it can give the max-the battery will not take 3 amps the entire length of the charge, usually). They “could” call it a 3000 mAmp charger. But why, when 3 amps does the same?
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