Animal stories refer to any fiction that features animals as main characters.
There are a number of realistic stories about animals living in natural environments; these usually follow one individual animal from birth to adulthood, or to death. Within this category there are stories told without dialogue and often without names (such as Chia, The Wildcat). The interaction between animal characters is usually confined to the business of establishing territory, mating, raising young, and (between different species) predation.
In other naturalistic stories, such as Tarka the Otter, the characters are named (sometimes simply by species name or an identifying feature), and there may be more interaction or some evidence of animal culture.
A number of these stories are children's books or short novels, such as Kit: The Adventures of a Raccoon.
Animals with culture
Other stories are about animals in a natural environment (or in a realistic one of domestic life or captivity) shown with their own culture, and their own language, histories and fables. Deities may be referred to or, in more fantastical novels such as Tailchaser's Song, be encountered. The characters still display essentially natural behaviour, although they are often more social and inclined to travel.
Watership Down is a well-known example, and other stories are often compared to it in reviews or descriptions.
Clothing and culture
In some stories, although the animal characters may not be described as being physically anthropomorphic, they do wear clothes and show other aspects of a defined culture, while remaining in a natural environment and dealing with natural dangers such as that of predators.
An example of this "Rabbits in waistcoats" genre is found in the characters of Owlglass by Will Nickless, where the Badger, Weasel, and similar characters live in burrows, albeit elaborately furnished ones, and strive to escape the talons of an Owl with whom they also socialize with. In Owlglass, the animals can clearly communicate with humans; this is not the case in all such stories.
Finally, there are stories such as Brian Jacques' Redwall series, where the animal's environment and habits show little or no relation to natural or wild life; some of these stories could be considered equivalent to (modern) fables.
Fables about animal characters are likely the oldest form of animal stories. These may be a way of describing desirable or undesirable behaviour, as in Aesop's fables. Animal fables also commonly deal with how animals came to look and act the way they do; the Old Mother West Wind stories provide an example.
Some animal stories are essentially satire, and although the characters have the physical form of animals, their behaviour can hardly considered animalistic at all, and are without the same significance as fables.
The Furry Novel List is divided into three categories: Animals behaving intelligently, "animals in their natural forms showing innate intelligence"; Intelligent Animals "Animals in their natural forms who, through methods scientific, magical or other, are able to express their intelligence in interactions with humans and/or other "intelligent" species."; and Intelligent Animalmorphs, or "anthropomorphic species".