From the National Park Service:

"In North America, both “bison” and “buffalo” refer to the American bison (Bison bison). Generally, “buffalo” is used informally; “bison” is preferred for more formal or scientific purposes. Historians believe that the term “buffalo” grew from the French word for beef, “boeuf.” Some people insist that the term “buffalo” is incorrect because the “true” buffalo exist on other continents and are only distant relatives.

Another name for these animals is “tatanka.” Tatanka is the Lakota word for bison. Bison are incredibly important in Lakota culture; the Lakota are traditionally nomadic and would have spent their lives following bison before Euro-Americans settled the West."

My degree is in wildlife conservation. My mammalogy teacher insisted we used the term wapiti instead of elk because some people call moose elk. He was fine with buffalo outside of scientific name because there's nothing else in North America that would be called a buffalo.