Germany, Deutschland or Bavaria?

Having spent nearly a week in what I would normally refer to as Germany, I have learned, like many things, our US perspective is not consistent with Europe.  First and foremost, the people of what we in the US call Germany consider themselves Deutschland.  That is how they will refer to themselves.  That is true for 15 of the 16 states within Deutschland.  Bavaria is the 16th state and has a unique position.  They never signed the constitution during the formation of Deutschland, so they are an independent state, with their own prime minister and flag.  So within the country, there are two prime ministers, Angela Merkel who represents 15 of the 16 states, and then the Bavarian Prime Minister.  However, as Bavaria is not recognized by the UN as an independent country, Merkel represents Deutschland to the outside world.  It does not sound like it is a divisive relationship, but definitely more complex than I understood before spending time here.