When you enter the Hero's Shade realm, the game stores which wolf you entered from, with an exception being the North Faron one. Upon exiting the Hero's Shade realm, you return to the stored wolf spawn location. However, the game uses 6 flags to know which wolf you entered from, and if these flags are swapped around, you can exit to different wolves, essentially "wrong warping."
In a practical setting, this can be performed by learning Ending Blow from a wolf other than North Faron, then going to another wolf that has a higher priority than the wolf you learned Ending Blow from. Upon visiting this wolf, select "I do not" to exit and Link will respawn at the site of the first wolf visited.
Currently there is no practical or advantageous use for Golden Wolf Storage (GWS) in runs, as it is dependent on exiting a wolf without having its own flag set (currently only possible with hacks). The game is checking to see if that particular flag is set, and the only way to set it is to get that particular golden wolf.
For more information on how this works with flags, check this pastebin: here.
Original discovery video:
Video on console: