Ok, but I still do not understand why the difference from 400/380 to 230 and in the case of USA 220 to 110.

Surely the frequency does not influence the voltage generated, provided the windings/lamination core are designed for the specific frequency.

Looking at how the center tap of a 3 phase alternator/motor is determined, I cannot understand how a different "formula" can be used for the two different systems.