During the James VI era, the crowns were separate. Both country had two different positions. James, just inherited the England as well (and he chose to live in London and rule from there, as it was the bigger city and hold more power).

If there was a different law in one of these countries saying that their monarch has to be, someone blonde for example, the crown lands would split from the personal union of the descendants of James.

But after 1707, the crowns were merged, the countries were merged into one. Great Britain. Still is today. British monarchs are monarch automatically of both states England and Scotland. The same kind of union happened between England and Wales, with more of a conquest way in the dark ages.

Another example to this could be when the British crown went onto Kings of Hanover. They were the closest protestant relative at the time, which us a whole different argument over Jacobite revolts. What happened was, King of Great Britain and Hanover was a personal union but Hanover had different laws of succession: no female monarchs. So when the British crown went to Victoria as the next in line, Hanoverian crown went to someone else. Therefore they split up. The union between these two crowns in a person is similar to what happened with James VI.