Animal class refers to any wildlife, no matter if that is native to Sanctuary or to any other world (provided that life form is not demonic or angelic). Some animals are even intelligent or semi-intelligent, and may even use magic. A corrupted wildlife form may or may not be an Animal, however, a savage demonic creature will not fall into this category.
Khazra, which are corrupted humans in essence, count as Demons in the second game, but as Beasts in the third game.
Undead may be risen from Animal remains if needed.
In Diablo II, Beasts do not exist as a marked category, but many enemies will count as Animals: Blood Hawks, Sand Maggots, Wendigo, Giant Spiders and Swarms, to name a few. They no longer receive altered damage from any specific weapon types.