These are either terms used on the site, or ones that are often encountered with dealing with these types of books.
Animal Fantasy: The literary term for a book starring sapient animals who still retain most of their animalness - their body shape and means of locomotion are what is normal for their species and they generally behave in the manner of real animals (except smarter). Novels of this type often create entire languages, cultures, and thought processes for their animal heroes, and these are classed as xenofiction.
Anthropomorphism: This term has two different definitions, both of which are used on this site. The more common usage is thus: Giving to nonhumans (including plants and nonliving objects as well as animals) emotions, personality traits, ways of thinking and levels of intelligence beyond what they are naturally thought to possess, thus making them more like ourselves. The second definition of "anthropomorphic," born on the internet, is as follows: A more literal 'humanizing' of animals, as in having them walk on two feet, wear clothes, drive cars and go to malls, for example. Bugs Bunny, for example, is an anthropomorphic rabbit in both senses of the word. These characters usually, but don't always (the "rabbits in waistcoats" genre being the primary exception), have far more humanlike anatomy than a regular animal of their species. The term is often shortened to "morph" and used as a suffix to denote a character is a being of this type: i.e., Bugs is a rabbitmorph.
Beast Tale: Generally used to refer to a folkloric or traditional tale, such as those told by Aesop, using animals to relate a moral to be applied to human existence. Few or no actual behaviors of the animals being written about will be on display.
Catgirl: Despite the name, they are not always cats, and nor are they always girls. A "catgirl," unlike an "anthro" or a "furry", is mostly human in appearance, but possesses a few prominent animal features such as furry ears or a tail. Some people do not consider them to be "anthro enough," but I personally do and thus include works featuring them here. Not often encountered, they're most commonly seen in manga (the Tokyo Mew-Mew series is a good example).
Funny Animal: A subclass of "morph" in which an anthropomorphic animal character is stripped of any instinct - or anything to add "animalness" to their behavior- and are reduced to mere human caricatures who might as well be human for all intents and purposes. Very common in cartoons, they don't make for the best characters to use in novels, in my opinion. Literary examples include the Arthur books and the Berenstain Bears.
Furry: A term with three definitions - the first two are the ones I actually use on this site. The first is a general term for anything - book, art, television show, video game, etc; featuring intelligent animals, both "morphic" and "nonmorphic". For example, Watership Down is an example of a "furry novel." The second use is as another term for "morphic" animal characters in general - Mickey Mouse, for example, is a furry. The creature doesn't have to have fur to be a furry - it's just a general term. The third definition, and the one I don't really deal with here, is a term to describe the online fandom (furry fandom) that has built up around those with an interest in anthropomorphic animals (which can range from the benign, to the perverted, to the spiritual). It's hard to define, as there's so many different types of people who identify with the "furry" title. I suggest going to another site if you want a really good explanation of the third usage of the term "furry."
Kitty Quest: A term for one of the most common of all types of animal fantasy stories - a story involving (obviously) cats on (usually magical) quests. Good examples are Warrior Cats, Victor DiGinti's Windrusher Series, Tad William's Tailchaser's Song, and Joy Smith Aiken's Solo's Journey. Although the best of them make for great stories, they are so common that some see them as cliche.
Manga/Graphic Novel: Basically, a comic book published in book form. Manga refers to comics that are Japanese in origin, while Graphic Novel refers to such publications from other countries. Many deal with sentient animals and/or morphs.
Morph: The "morph" suffix when applied to a species in the book listings on this site is used to denote that the animals (or animal-like aliens/creatures) in the book are bipedal and either physically built like humans, or dress and act like them.
Otherkin: Although it has a very different definition when applied to the online community of this name, when it comes to anthropomorphic fiction, "otherkin" based books are ones featuring either "normal" or "morphic" versions of imaginary animals such as dragons and unicorns. Robin Wayne Bailey's Dragonkin series is a very good example.
Encounter any other anthropomorphic related terms you don't understand on the site? Drop me a line and let me know about it, and I'll add a definition here.