In fact, the confusion is common. But furry refers to anthropomorphic animals, bestial refers to purely animalistic beings, kemonomimi refers to humans with features like ears and tails, and demons are similar; none of these fall under the furry category.
Furry: An animal with a human body and mind. Kemonomimi and demon: Humans with slight animalistic features. These include kitsune, werewolves, and even oni.