ok, so if we in the U.S. are geographically challenged, please en- lighten us...what about this statement is incorrect?

"Ireland, or Scotland, or Britain...I know why Americans so often have such screwed-up geography as regards this part of the world."

I think the British Isles includes Scotland, England and Ireland, am I correct? Does U.K. mean "just" England? then what does the United part stand for? Is there a difference between Britain and England?

If we need more info, please provide it! thank you...
trying to bridge the gap between UK'ers and US'ers.