The power uses the un-used potion of the 8 wire cable, here is a simple explanation.
Ahem cough splutter, is that the sound of someone asking to be corrected ?
Only FE uses two pairs.... GE requires all four !
Your understanding of the theory is wrong ... PoE is more comparable to ADSL which magically allows you to use broadband and make phone calls at the same time, not forgetting of course the fact the phone company is also sending voltage down your line too !
It is unfortunately a widespread misunderstanding, which indeed renders many cheap PoE injectors
INCOMPATIBLE with Gigabit ! So
caveat emptor if you're running Gigabit and are thinking about being stingy on PoE injectors !
PoE uses a phantom power technique. Similar in concept to what you find in lav mics.
IEEE 802.3 if you need bed-time reading.