"Bison" is an European word (with several variants like "Wisent"), so it makes sense that originally it was the name of an European animal. It became applied to the American bison when the American colonists have encountered an animal similar to the one known by them in Europe.
The European bison is a distinct species from the American bison. In the more distant past bisons were widespread all over the Northern Eurasia and Northern America. They have been preferentially hunted everywhere, so their populations have dwindled and fragmented, becoming isolated, then they have become differentiated.
The European bison is somewhat smaller (because it had been mainly a forest animal) and it had become completely extinct in the wild a century ago.
Fortunately, there were enough captive, which have been bred and then reintroduced in the wild in some of their former territories, e.g. in Poland and Romania.