In international law, "state" is probably the correct term for a sovereign governmental entity. Nation is more of a cultural term. Thus one "state" could have many "nations" in it in a multi-ethnic empire - for example the old Soviet Union, Czechoslovakia or Yugoslavia. You might even argue Iraq and the United Kingdom are that way right now. Similarly, you could have one "Nation" split into multiple "states" like East and West Germany. The trend in the past century has been for the "states" and "nations" align.
We run into the problem of using the term "state" in English to also mean political subdivision in addition to sovereign government. There is no good English word meaning sovereign government and nothing else. State, nation and country all fall short.
France is a Nation
Britain is an Island
Egypt is a River
Germany is a Language