Different materials used as basis for different battery techs will produce different voltages when the ions go to the anode (something to do with the energy that can gained when the ions combine with the material of the anode being only one of a fixed set of possibilities due to the available free bands in the atomic structure - please check Wikipedia for a proper and correct explanation rather than my vaguelly remembered one) which is why Lithium batteries are always around 4V without extra electronics to drop the voltage (which make them less efficient) and voltages above that require putting multiple cells in series to add their voltages.

As it so happens, the techs for the Carbon-based, Alkaline and Cadmium all have this voltage be around 1.5V (though you might have noticed that the Cadmium ones are a little lower than 1.5V and Alkaline a little higher) so you need 6x cells in series of batteries of that tech to get 9V.

That I know of, there is no consumer battery tech which has a single cell voltage of 9V and I don't even know if there is any substance or combinations of substances that makes that possible at all.

pretty much, yeah. A 12V is pretty much just 10 1.2V cells iirc