When I've heard the distinction (often in a historical context), 'nation' is usually meant to mean a set of people in a place with some sense of collective identity or origin, while 'state' is the governing body which has a monopoly on the legitimate use of violence within well defined borders. When these overlap the result is a nation-state, but they don't always line up so nearly. Using those definitions England, Wales, and Scotland are nations. Ireland (including northern Ireland) could also be called a nation (though, of course, as should be obvious by the fact that this does not line up with the borders of the state, this is a contentious topic). The United Kingdom is the state (and of course Ireland-minus-northern-ireland is also a state). 'Country' as a term generally doesn't imply either of these (it's just a name for some chunk of land, notionally), though it's often synonymous with the nation-state when the borders all actually line up neatly, as opposed to in the UK.