Its rather simple.....
The United Kingdom of Great Britain and Northern Ireland as its full title is, is a political state that is composed of four constituent nations, the England, Scotland, Wales, and Northern Ireland. each of these areas while not politically independent have their own cultures, languages, histories, and in recent years devolved political structures.
Great Britain is the name of the island that is composed of Scotland, England and wales, and has no real political meaning, though it is incorrectly substituted at times for the United Kingdom. (much like America is often used instead of the United States of America)
There is a British parliament over all of the country based in Westminster in London.
The British Monarchy actually come from a German royal line.
Charles is actually prince of Wales, this is historic title for the next in line to the British throne.
William is actually only Duke of Cambridge....
(hate the nonsense of the royals but thats a different story.)