I'm American and always wonder why so many Americans can't get the simplicty of the differance between England, Scotland, or Wales.
Here in the States New Yorkers are New Yorkers, NOT Pennsylvanians, Californians, Texans, or Floridians. In the UK it's the same.
For my fellow Americans, here is a simple way to remember it showing the somewhat equivalent terms used on each side of the Pond. I know these are not 'exact', they are close enough for comparison.
US/United States -> UK/United Kingdom
(I used the shortened versions for both countries.)
American -> Briton, or more informally, Brit
This next part is a little tricky:
Marylander, Texan, Georgian, or any other state ->
-> Englishman, Scotsman or Scot, Welshman, BUT, they are normally refered to as The English, The Scottish, and The Welsh. (Yes, I know I left out the good folks from Northern Ireland.)
I can say 'I am a Pennsylvanian,' which I guess would be comparable to 'I am an Englishman, or Englishwoman.' Interestingly enough, in the States, people from the New England states are New Englanders, not New Englishmen. Isn't English a fun language? lol
Anyone from Britain feel free to add to or correct any mistakes I made, but I was really just trying to explain the basics.