Technically they are two different things, in the language of political science. I'm don't know exact definitions, but a nation is something a group of people have an emotional attachment to, a cultural entity; a state is a political entity. If you're lucky, the two coincide and you a have a nation state.

The U.S. usage of 'state' has a different meaning. Maybe when the states were more independent entities (with their own currencies, militias, etc.) around the time of the Revolution, it carried the standard meaning.