They talk about nations, not states. They aren't the same thing. If a nation attacks the United States, the United States is at war. An entity such as a recognized state or country is not required, a nation will do: The stateless nation of terrorists.
I think you have hit on a key distinction. Nations are indeed different than states, the terms Cherokee nation, Sioux nation and the Nation of Islam come to mind. Words ,and their definition, are not only crucial in the diplomatic realm but in the every day language of discourse. We have lost the ability to understand that common usage does NOT negate the original meaning of words that were coined. I remember when gay meant happy.