Don't ask me why the Great was added - I guess this was just a throwback to the Empire when they actually thought they were great. I'm sure the people of Amritzah in India or Maoris in New Zealand wouldn't agree. In this agreement Scotland arranged to keep many of it's traditional institutions including it's own legal, educational, religious establishments but, to be honest, a lot of Scottish people don't understand the constitutional differences between the two countries. For instance all citizens hold British passports, but sometimes say they come from the UK, Scotland or Britain. Further confusion, and a huge source of annoyance, comes from the fact that many people outside of the UK refer to the whole UK as England.
Nothing is guaranteed to upset a Scottish person more as referring to Scotland as England.
In the Union of the Parliaments Scotland and England were to be 'full and equal partners' in the Union but this has never been the case in real terms. In line with many partnership agreements Scotland has suffered as a lesser partner to England and has had a real identity problem since 1707. This identity problem is nowhere more apparent than in the flags of the country. Contrary to popular belief England's flag is NOT the Union Jack. When you join them together you get the Union Jack.