A nation is a group of people with a strong shared culture. An example of a nation without a State is Kurdistan.
A state is a political organization that may or may not also be a nation. An example of a State that was not a nation was the USSR.
What we call the Palestinian people today certainly have never had a State; they also don't meet the definition of a nation- they are a bunch of nomadic tribes that got stuck in what is now Israel during the confusion after WWII. They are the pawns of the Arab states, who could easily absorb them if and end this nonsense.