What different types of werebeasts are there?
None. But you didn't really think there were, right?
"Were" is an old English term meaning 'man'. Werewolf mean 'Wolfman' (or, properly, man-wolf). Mythologically or in terms of roleplaying games such as Dungeons and Dragons, there are Werebears, Werewolves and probably wome other Werecreatures as well but there is no such thing as a werebeast outside of legend and gaming. Check the Monster Manual for a list of Werebeasts Gary Gygax et.al. have developed.
Legends of shape-shifting and/or adopting animal characteristics are very old indeed and exist in almost every culture worldwide. The specific legends of Werewolves as we in America generally understand them are European in legend and there is documentation of these legends dating back at least to medieval times.
Following is lifted from Wikipedia about the history of the Werewolf Legend. For more, search Wikipedia.org:
"Many authors have put forward the idea that stories of werewolves (and vampires) may have been used to explain serial killings in less enlightened ages. This theory is given credence by the tendency of some modern serial killers to indulge in practices (such as cannibalism, mutilation and cyclic attacks) commonly associated with the attack of a werewolf. The idea (although not the terminology) is well explored in Sabine Baring-Gould's seminal work The Book of Werewolves.
A recent theory has been proposed to explain werewolf episodes in Europe in the 18th and 19th centuries. Ergot, which causes a form of foodborne illness, is a fungus that grows in place of rye grains in wet growing seasons after very cold winters. Ergot poisoning usually affects whole towns or at least poor areas of towns and results in hallucinations, mass hysteria and paranoia, as well as convulsions and sometimes death. (LSD can be derived from ergot.) Ergot poisoning has been proposed as both a cause of an individual believing that he or she is a werewolf and of a whole town believing that they had seen a werewolf.
However, this theory is controversial and not well accepted.
Some modern researchers have tried to use conditions such as rabies, hypertrichosis (excessive hair growth over the entire body) or porphyria (an enzyme disorder with symptoms including hallucinations and paranoia) as an explanation for werewolf beliefs. Congenital erythropoietic porphyria has clinical features which include photosensitivity (so sufferers only go out at night), hairy hands and face, poorly healing skin, pink urine, and reddish colour to the teeth.
There is also a rare mental disorder called clinical lycanthropy, in which an affected person has a delusional belief that he or she is transforming into another animal, although not always a wolf or werewolf.
Others believe werewolf legends arose as a part of shamanism and totem animals in primitive and nature-based cultures.[citation needed] The term therianthropy has been adopted to describe a spiritual concept in which the individual believes he or she has the spirit or soul, in whole or in part, of a non-human animal."
Werebeast stories differanciate depending on where you are.like in places that harbor bears but not wolves, there might be stories of werebears insted of werewolves.