I think youre right, ATX 12v has the 20 plus the 4 pin 12v connector, ATX 12v ver 2 has the 24 pin and no separate 4 pin 12v connector, looks like they just moved it to the main connector.
The regular plain ATX is just the 20 pin with no 4 pin 12v connector then.
They get use interchangeably a lot Im sure.