A good way to look at it is that apocalypse wolves are super soldiers of Gaia and forsaken wolves are keystone predators of an intricate supernatural/spiritual ecosystem.
pretty much everything, it's a completely different setting. but basically the focus is much more personal as there isn't some vast cosmic war, werewolves are the guardians of the border between the spirit world. only five playable tribes, which are ideological/focused on hunting specific threats.
Werewolf: the Forsaken, 2nd edition in particular, is amazing and Paradox making it so that it doesn't get any more official support should have been a crime. But at least we have the ST Vault and the Patreons of some of the developers still giving us good Forsaken/CofD content.