State - occupies space with borders, political sovereignty, international recognition, has people (the countries below are all states)
Nation - people who share a common ethnicity, language, religion, history, etc. Examples: Kurds, Palestinians, Basque, Saamis
Nation-state - ONE group who is also sovereign, France or Germany in previous years before immigration, closest today is Iceland or Japan
Multi-National State - everywhere but perhaps Japan and Iceland, has a mix of people
Stateless Nation - there can be thousands of these, Native Americans are all statless nations, no official borders or sovereignty, Palestine, Tibet, Basque are all examples, the largest stateless nation by population are the Kurds (30 million people spread in 6 countries.
Multi State Nation - people with a shared culture and spread over several states, may need or want a nation at some point, examples are the Jewish people or the Koreas