What is a Furtaur? 
A Furtaur is basically the same thing, only the top half of the body is an anthropomorphic animal, and the bottom half, rather than being a horse's body, is the common four-legged version of the a fore mentioned anthropomorphic animal. For example, a 'Tigertaur' would be a centaur with a tiger's body in place of the horse's, and an anthropomorphic tiger where the human's upper body usually sits (where the head and neck of the tiger should be). Furtaurs are also called, simply, 'Taurs. 

How did 'taurs come to be? 
[Best read if you are scientifically literate!] 
All animals' DNA is coded in segments. For example, an insect has three segments; head, thorax, abdomen. A spider has two segments; cephalothorax [head and thorax combined], abdomen. This holds true with virtually every animal, from humans to slugs...at least as far as DNA is concerned.  

A common mutation in fruit flies causes them to be born without antennae. Instead, they grow an extra set of legs on their heads. This is because their "head-segment" started out with feeler-legs which became modified as antennae. The most basic DNA in their body says "leg on segment X, leg on segment Y, and leg on segment Z", while another genetic code in more recently acquired DNA will modify that with another instruction which states "leg on segment X is to form an antennae". When the more recent DNA fails to be activated, the insect is left with a leg instead of an antennae, which is considered a recessive gene.  

Which brings us to the mammalian and reptilian 'Taurs. Basically, a mutation in DNA sequencing caused members of several species to grow an extra segment on their body. Because the ancestors of 'Taurs were already walking upright (they had become anthropomorphic), the ancestral DNA was placed in the middle segment. 

For example, an Anthro's DNA might state "front limbs modified as arms", where as the "extra-segment" gene causes confusion in the DNA, the "front limbs modified as legs" (the trait carried by four-legged animals) would establish itself in the middle segment, upon which a secondary pectoral girdle (shoulder blade) would over-lap the existing one and act as a set of hips to anchor the upper body of the creature, which carried the instructions "front limbs modified as arms". 

In short, the hind segment still had hind limbs, the middle segment had the front legs of that creature's ancestor, and the foremost segment had the more modern-looking front limbs (arms). 

Another way of stating this is; 
 

This mutation proved lethal in many species, but some managed to survive. Birds for instance, were not able to survive as 'taurs because the stage which preceded their wings were arms - birds started out as bipedal dinosaurs, which did not walk on their front limbs. Nor did the reptiles which preceded dinosaurs. The 'taur-gene simply asked too much of the existing bird-DNA for them to survive. However, the 'normal' anthropomorphic birds were fine.  

How/Why did this mutation occur in so many species? 
The same nuclear wars which killed humans left our planet scarred with thousands of localized nuclear winters. A wide variety of mutations actually took place in several animals, however the only 'disfiguring' mutation that proved beneficial was the 'taur-gene. All other mutations were either harmful or neutral, and were therefore not preserved.  

When did Furtars come about? 
They occurred separately in each of the species affected over a span of twenty million years, while each anthropomorphic creature was going through a stage similar to the humans' Australopithecine (upright ape) ancestors. (See the Backstory)