In the part 2 of the Shieldstravaganza, Robert talk about the ethernet shields. The first one (at 0:55) is the Sparfun PoEthernet shield. (DEV-10864). The second one (at 5:20) is the oficial Arduno Shield with de PoE Module. (DEV-11230).
The Sparksfun shield uses pasive "unoficial" PoE, inyecting power over the 7,8 (+) and the 4,5 (-) pins. You still need a PoE inyector and a power source to put the power in the ethernet cable. The Arduino shield uses the "standart" IEEE 802.3af. This way, uses a PoE source (mainly ethernet switch) to put the power in the cable. This schema modulates the data using the same cables used to the PoE. In gigabit ethernet, all 4 pairs are used, and still is posible to use "official" PoE.
Those two ways to build a PoE circuit are compleatly diferent, and not compatible.