is the nation and the state very different ideas?

Yes, they are very different concepts, although the terms are often used interchangeably.

A state is a political construct, an organised political community, with a form of governance- a state may be sovereign, but not necessarily.

Since the 19th Century the word nation has become shorthand for a country - but is is not always so.

The concept of a state composed of people who share a common language, ethnicity and culture did not really exist before the modern era. That's not to say that they did not exist, rather that the idea of "belonging" to a political entity was based more on localism - to your lord or king, rather to your fellow countrymen.

For example, Shakespeare, in Richard II and in Henry V uses very powerful language that appears very patriotic, and certainly patriotism was a powerful force. But both Richard II and Henry V ruled areas that are now French, and people in these areas would have not felt English, rather they would have felt loyalty to their region - Anjou, Gascony or Normandy, and, more specifically, to their lords.

The state was embodied, not by the people but by the monarch - Louis XIV said "L'etat, c'est moi", "I am the State".

In modern times the concept of nation is still a difficult idea to grasp, there are exceptions to every model proposed. For example, if common ethnicity is the model for the nation, then Belgium, Switzerland and the UK are not nations. If it is a common language, again, Belgium, Spain and Switzerland are not nations. If it is a shared sense of history, then Britain (as an amalgam of 4 countries) is not a nation. If it is a shared culture and / or religion, then Spain, Switzerland and Belgium are not nations.

I think that the French philosopher Ernest Renan sums up the concept of nationhood most succinctly in his 1882 work Qu'est-ce qu'une nation? ("What is a Nation?"),

"A Nation is a soul, a spiritual principle." and

"A nation is therefore a large-scale solidarity, constituted by the feeling of the sacrifices that one has made in the past and of those that one is prepared to make in the future"

yes