How can you compare a generator to a battery? How do you charge the battery without a generator?

Betavoltaics aren't really either - they provide a constant, slowly-over-years declining flow of power. They can't be recharged, they _could_ be refueled (don't know if it's economic though), and are mostly used when you need a small flow of power and a long period of time between maintenance (think pacemakers, weather buoys, some satellites or probes).

A bettery, from the viewpoint of a circuit, is just another source. So we could call them chemical electricity generators, if we're brave enough to indulge the confusion

I still don't quite understand it. Where does the battery get the energy? I understand that there's no difference in a circuit, but why is this comparison relevant? Many power sources are way less efficient that using a battery, but we need to charge the battery.

Alkaline batteries are never charged, per se. The energy comes from the one-way chemical breakdown of cathode and the anode.

For low-enough-power applications and sufficiently long-lasting batteries, charging is just another step in production.

Betavotaic generators usually produce extremely low power. A similarly sized battery can last for decades at the same power output.

I believe GP means a disposable battery that you replace with a new one when it's empty. Not a rechargeable battery.