Really depends on the region and any pre-existing constraints at the time of electrification. A better distinction is probably rapid transit (metro, subway, the Tube, MTR/MRT) vs commuter rail.

Apparently in the US there are trains that use dual rail and overhead power, one for subway and another for overground portions.

I suppose a subway train with rail only supply that goes overground sometimes is more dangerous because it is easier to accidentally step on a rail and rail is powered?

This is common in London as the suburban rail network there is a mix of third rail and overhead lines.

Not in Tokyo. All but the first two of Tokyo’s subway lines run on overhead wires. In fact they had to build most of the subway lines to suburban rail standards because they planned on operating through services in the beginning.

Typically, trains power themselves.

Also not really true. There are trains all over the world that draw power from over head lines and from 3rd and 4th rail systems.

I design rail systems. That is not true, except maybe in your city.