They use different chemicals that result in different voltages. The voltage is the result of a chemical reaction and the voltage depends on the chemicals
The common AA sized non-rechargeable are Alkaline batteries with Manganese (IV) oxide cathode and Zinc anode that result in a nominal voltage of 1.5V
The common AA sized rechargeable uses a Nickel oxide hydroxide cathode and in principle, a hydrogen anode is the form of a Metal hydride. That result in a nominal voltage of 1.2V
Both types might be the same physical shape but the content if different. For most application a 1.2V battery will work even if it was designed for 1.5V but there are esceptions.
None electric cars have lead-acid batteries with Lead dioxide cathode and Lead anode and the nominal voltage for them is 2.1V. You have 6 cells in each battery for a total of 6*2.1 =12.6V but as just called 12V
The most common rechargeable batteries today are likely not at 1.2V but at 3.7V as that is the nominal voltage of common Lithium-ion batteries. The use of different kinds of lithium cathodes like Lithium cobalt oxide with a Graphite. Cellphones and other devices with build-in batteries use them. This is the type of battery in an electric cat, you just have a lot in series to get to the voltage for the engine that is around 400V
There are Li-ion batteries with the same shape as a AA battery at 3.7V but they are called 14500 batteries. Some flashlights can use both but they likely would kill a lot of other devices.
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