All murdered souls arrive in limbo at the Gate of Grudges, where the Gatekeeper, Izuko, presents them with a choice: they may pass through the Gate into Heaven; they may cling to life on Earth and remain a ghost there forever; or, they may haunt and kill one person in exchange for eternal damnation. As each spirit passes before the Izuko she is bound to explain these options and impartially accept their decision; what will each choose? Peace, or spending an eternity in Hell?
The biggest difference between these two is that in Skyhigh, the people who have grudges are already dead. Both are very similar -- people who have been wronged chose between eternal damnation or moving past their grudge. In Hell Girl, the living invoke Enma Ai to do their bidding, but in Skyhigh they arrive at the 'Gate of Grudges' and determine there whether they'd like to move onto Heaven, cling to Earth in limbo, or get one last chance to get back at someone and in return, suffer eternal damnation.