http://en.wikipedia.org/wiki/Countries_of_the_United_Kingdom
I don't think many people answer "British" to the question "What country are you from?".
If you asked me what I am, I might respond "British" - whereas if you asked where I'm from, I might respond "Britain".
Oh and good thing my terms are German-centric, since I'm French. We don't even have the notion of state here in our civic system (but we do have tons of others of course).
That's not true in general. People in Northern Ireland are entitled to one or both citizenships which makes it true in that limited case.
http://www.electoralcommission.org.uk/faq/voting-and-registr...
"To vote in a UK general election a person must be registered to vote and also [...] be a British citizen, a qualifying Commonwealth citizen or a citizen of the Republic of Ireland"
http://www.dublincity.ie/yourcouncil/votingandelections/Page...
"Elections for Dáil Éireann: Both Irish and British citizens can vote in elections for Dáil Éireann (the lower house of parliament)."
The Commonwealth shares a head of state; for example, Canada would be a sovereign state (small s) within the terminology of the Commonwealth. The Common Travel Area has passport-free travel; Irish and UK citizens can vote in one another's national parliaments, while EU citizens generally can only vote in local and EU elections. British crown dependencies are distinct from its overseas territories. There aren't enough shades of meaning in the miserly handful of terms you defined above (and seems rather German-centric) to adequately cover all the dependent and independent relationships involved.