Interestingly, if Scotland becomes independant, but retains the Royal Family, they remain within Great Britain a term which was coined after the union of the crowns before the union of the countries. The term United Kingdom of Great Britain was not used until after the union of the two countries and after the union of the two Parliaments.
Britain is a derivation of the Roman name of an area they controlled; 'major' for the parts of theses islands and 'minor' for the parts now in France - Brittany now. The parts of our islands included areas north of Hadrian's wall, not all of what is now Wales and most of what is now England. To equate the Roman term Britain to current political boundaries is rather pointless. To be British is to be a subject of Her Majesty and from Great Britain, thus someone from an independant Scotland under the crown would still be British as well as Scottish whether we, or they, like it or not.
Pedant hat now off!