The voltage depend on the chemisty used in the battery. Each atoms has a diffrent [https://en.wikipedia.org/wiki/Electronegativity](https://en.wikipedia.org/wiki/Electronegativity) that is the binding energy if a electrons. It result in diffrent [https://en.wikipedia.org/wiki/Standard_electrode_potential](https://en.wikipedia.org/wiki/Standard_electrode_potential) for a reaction. The battery voltage is a the diffrtence in the potential of the the reaction. The voltage for Nickel–metal hydride and the older nickel-cadmium are nominally 1.2V. In a alkaline battery the reaction is diffrent and you get 1.5V nominally.
It is not really a question of rechargeable vs non-recagable. Ther are Li-ion batteries in the common AA and AAA form factor, they are recagable with a nominal voltage of 3.7V. They are typical called 14500 for AA form factor and 10440 for AAA to reduce convulsion. The name are from the size, a 14500 battery is 14mm in diameter and 50 mm long,
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