W.hat characteristic does a nation have which distinguishes it from an ethnic group?

A government. In contemporary English usage, "nation" usually denotes a state. At one time, it did mean essentially the same thing "ethnic group" does now, but the meaning has changed over the years. That's why we had to invent the term ethnic group to replace it. Actually "nation" and "race" both used to have that meaning, but they've obviously both been redefined.