Answer:
Not too much, really. Bison are commonly referred to as the large-humped, small hollow-horned, furry-headed beasts that existed by the millions on the Great Plains (called the Plains or American Bison I believe) and are also found up in northern Canada as Woodlands Bison. Bison of North America are also called Buffalo, but bison has been created as a more proper term, since there are "true" buffalo that exist in the world, such as the Cape Buffalo and the Water Buffalo, both found in Africa and India, respectively.
On the humorous side
There really isn't any difference, with the exception that you cannot wash your hands in a buffalo.
Think about it a bit. You have to be British to understand the differentiation.