It seems strange in our modern world of clearly defined and organised nation-states, but the concept of two countries being ruled by the same person but also being independent in other regards was quite common in the Medieval era and Early Modern era. Essentially the head of state/head of government was the one monarch (e.g. King James VI/I), and he was the undisputed ruler of the country. However, each country would still retain all or most of its separate institutions. To use the example of Britain, both England and Scotland had their own separate parliaments and churches (i.e. the Church of England, and the Church of Scotland) that passed their own legislation and approved its own doctrines. These institutions were filled with the native people of their country, and there was very little to no placement of foreigners in their ranks (i.e. from the other country that the king ruled). Such a thing would have been completely unacceptable and resulted in a revolt. It was common for there to be differences in legislation/laws/religious doctrine between England and Scotland in this era, sometimes even very major, because the English Parliament could not force the Scottish Parliament to adhere to its policies, and vice versa. King James was the only connecting factor between the two, and as he was a shrewd and level-headed monarch he rarely ever tried to force one parliament to bend to the will of the other. He may have spent more than twenty years living and ruling in England, and preferred living there than in Scotland (mostly due to England being the larger and stronger country), but he was still a Scotsman and had ruled Scotland for decades before coming to England. He was the last person that would ever infringe on Scotland's independent status.

To see what would happen if the king forced one country to follow the laws of the other when it didn't want to, one only needs to look at the English/British Civil War, which occurred in the reign of King Charles I, the son of King James. Charles - who only ever lived in England - had created his own Book of Prayers which was popular in England but unpopular in Scotland. He wanted both countries to adhere to it, but the Scottish Parliament and Church refused. He went so far as to threaten military action to force them to accept this Book of Prayer, and the Scots refused to back down, and thus the civil war started (there were other factors that caused tension in the build-up to the war but this was the triggering event). This shows that even though a man may be king, he was not all-powerful; Scotland, with the support of its parliament, church and nobles, successfully resisted the imposition of English religious policy when it was not wanted. Charles fashioned himself a modern absolute monarch with a divine right to rule how he wanted, but the medieval traditions of strong regional autonomy, which continued until well into the Early Modern era, successfully fought back. A king might order something to be done, but if the majority of powerful political figures in this country refused to go along with it, and they had the support of the army, then the king would not be obeyed.

Similar types of events/conflicts occurred in other parts of Europe where a single monarch ruled over nominally independent countries, such as the King of Spain ruling over the 'separate' kingdoms of Castile and Aragon (which has interestingly continued into even the modern day, with these kingdoms still officially being independent parts of a greater whole); the King of Poland also being the Grand Duke of Lithuania; the Habsburg emperors being both the Emperor of Austria and also the King of Hungary, etc. There was naturally always one country that was in a slightly subordinate position to the other, just by the realities of military, political and economic strength disparities, but centuries of deeply ingrained traditions of regional autonomy were almost impossible to stamp out fully; in 1868, for example, the Emperor of Austria, Franz Joseph, was forced to recognise Hungary as an independent country on equal terms with Austria, and he could not force Austrian-centric legislation onto them whatsoever. This came after centuries of Hungarian opposition to centralised Habsburg rule, and many large-scale revolts. But following this compromise, he no longer had any trouble with Hungary and they were the most loyal part of the Habsburg empire. Such movements for greater regional autonomy, or 'federalisation', was seen several more times in the late 19th to early 20th centuries in other non-German parts of the multi-ethnic Habsburg empire. These provinces were fine being ruled by Emperor Franz Joseph, but they wanted him to rule as the King of Croatia, or the King of Serbia, for example, and not the Emperor of Austria. It may seem like an arbitrary distinction to our 21st century minds but it was deeply important to these people at the time. And that was the whole crux of the issue.