Nation and state appear at first to be effectively identical concepts, both denoting a sovereign territorial entity and its society. American journalistic and informal usage perhaps favors "nation" simply to avoid confusion with "states" like Iowa and California. Often in fact the combined form "nation-state" is used, as though to clarify what sort of state is intended.
However, nation and state are not in fact quite the same thing, and the difference has dramatic consequences. State is the preferred word in formal discussion of international relations, because it is a formal, legal concept: a sovereign territorial entity. It may be true in practice that sovereignty is never absolute, but provides a conceptual bright line.
Iraq is a state, even though it currently exercises no sovereignty, but is governed by an occupation authority of other states. This condition is presumed to be temporary. Iraqi Kurdistan is not a state, even though it enjoys very considerable autonomy within its territory. Its autonomy is presumed to be, if not temporary, at least contingent, and in the long term an internal Iraq matter. That is, Iraq might emerge as a federal state, within which Kurdistan continues to enjoy some autonomy, but "invisible" and irrelevant to the international system in the same way that Texas is invisible to the international system.
Nation, however, has a more ambiguous meaning. In everyday usage we do use to mean a sovereign territorial entity, i.e., a state. But it carries an overtone of a society, a community of people who identify themselves with the nation. Since the rise of nationalism as an ideology, the belief has been strongly and widely held that nations should also be states. This has become the expected norm. Sweden and Thailand are states; we also understand them to be nations, whose people speak Swedish and Thai, and participate in Swedish and Thai culture.
However, a nation is not ne...