Reviving this old thread only to ask you to confirm if the difference between those two is as simple as that: państwo= state and kraj= country. I thought that there was a subtler difference, as is the case with anything else in Polish :S Look forward to your answers, thank you as usual.
"Kraj" is a very universal term, similarly to the English equivalent ('country'). In a colloqial speach it can refer to the state, but often it refers to large regions or historical entities.
Although the examples quoted by Drakonica:
"Kraj Przywiślański" was one of names of Poland as a part of Russian Empire.
"Kraj Krasnojarski" is a part of Russian Federation.
are translated from the Russian language, so in a sense they do not count, but the general idea is correct.
"Kraj" is also used as a translation of the German "Land" - so in Polish we say about "kraj związkowy" for example (Bundesland, if I remember correctly).
"Państwo" sounds a bit bookish. It's used in the official documents, and in a colloquial speach mainly if you want to be precise that you mean a national state rather than a historical or modern region.
BTW - in the context of the United States of America and other American Federal states (Mexico and Canada come to my mind), the "state" is translated as "stan" rather than "państwo". In Polish Alaska or Texas (states) are "stany", and the USA ("Stany Zjednoczone Ameryki Północnej") are "państwo". Germany (Bundesrepublik Deutchland) is also "państwo", but the lands it's comprised of ("Land" in German) are called "kraj" in Polish - the two are federal states which are best known in Poland.