Home Assistant Yellow - PoE vs PSU version

It is unclear what is the difference between the Home Assistant Yellow versions. The one says PoE and is more expensive, while the other one includes a power supply and is cheaper. The description says the board can be powered by either. So what is the difference between these two? Why is the PoE version more expensive? Does it come with a PoE injector rather than a power supply? And does the PoE version also include a power supply, or not?