I found older posts with battery-related questions regarding charge or replacements, but I am trying to understand how inventors/developers determine which type of battery to use with certain devices.
Two factors are in play:
1) The form factor of the device being powered.
2) The power requirements of the device.
AA, AAA, AAAA, C and D are all 1.5 volt regardless of their size. CR2032 (the circular button shaped battery) outputs 3V and 9V doesn’t need explanation.
If you have a remote control that requires 6V to power the electronics inside of it. You’ll need to use 4 A-D batteries (1.5V + 1.5V + 1.5V + 1.5V = 6V). D and C batteries are too big for remote controls, but A type batteries are just the right size. Whether the remote uses AA or AAA or AAAA depends on the shape of the remote, but it can be an arbitrary decision in many cases. If you are powering a flashlight, you might opt for C or D batteries since form-factor is less of an issue. Four D batteries in sequence will output 6V, just as four AA/AAA batteries do. However, because D batteries are bulkier they have more juice. This will makes them last longer inside a flashlight as opposed to 4 AAA batteries, which would also fit inside a flashlight and power it, but not for very long.
They look at how much power the device needs to consume, and try to pick a battery big enough to power it for a conveniently long time, but small enough to avoid making the device too big/heavy.