"...you mean that when I set up a cartridge on one arm with, say.....Baerwald geometry......it doesn't mean that it will be correct if I change to another arm with a different pivot to spindle distance and overhang?"
Yes; it will not be correct. But your tonearms are vintage Japanese types. Many or most of those were designed with Stevenson geometry in mind or with some idiosyncratic geometry unique to that tonearm (e.g., SAEC 308SX). You can use Baerwald alignment for some of them (not SAEC 308SX), if you must, but the cartridge will end up twisted with respect to the long axis of the headshell. My experiments with doing that did not sound good. But no matter what geometry you use, a given alignment of the cartridge will work in two different tonearms only if they have the exact same P2S distance, effective length, headshell offset angle.
Yes; it will not be correct. But your tonearms are vintage Japanese types. Many or most of those were designed with Stevenson geometry in mind or with some idiosyncratic geometry unique to that tonearm (e.g., SAEC 308SX). You can use Baerwald alignment for some of them (not SAEC 308SX), if you must, but the cartridge will end up twisted with respect to the long axis of the headshell. My experiments with doing that did not sound good. But no matter what geometry you use, a given alignment of the cartridge will work in two different tonearms only if they have the exact same P2S distance, effective length, headshell offset angle.