Most monarchs are the king or queen of a country (Queen of United Kingdom, King of the Netherlands), but in the middle ages there were also some monarchs with a title such as 'King of the Germans' or 'King of the Scots'. Does this distinction have any meaning and who decided the title?
Apocryphally, the distinction between being the monarch of a people and the monarch of a kingdom, or land, was the distinction between being the acknowledged and accepted ruler of the people by the people versus having an inherent and divine right to ownership, and therefore governance, over a large geographical area and the people residing in that area. In the case of Scotland, this distinction has been used to support the notion that the Scottish monarch is only a first among equals (his or her equals being the Scottish nobility), and thus, replaceable if s/he is not perceived to be fulfilling the duties of a monarch adequately. There was another question posted here recently by u/Khwarezm about the violent nature of Scottish kingship in the late middle ages that speaks to this issue as well (see: https://www.reddit.com/r/AskHistorians/comments/ggztxh/why_did_late_medieval_scottish_politics_seem_to/ for some other great perspectives and answers to the question of political violence by u/lngwstksgk, u/wishbeaunash, and u/acuriousoddity ), and there was certainly an element of this rhetoric of kingship present in Scottish ideas about monarchy throughout the medieval and early modern period.
Notably, the justification of the Declaration of Arbroath (1320) where the bishops and nobles declared that they had an absolute right to choose their own monarch to justify their resistance to English rule under Edward I relies on this notion of the Scottish king being the king of Scots, rather than the king of Scotland. The same rhetoric is present in the deposition of Mary, Queen of Scots, and in the execution of Charles I for "treason against his office" in 1649, though by then, Charles Stuart was king of England and it was the English who used inadequate rule to justify regicide rather than the Scots, who themselves were irate at the execution of the king.
That said, if we look at the charter evidence across the medieval and early modern period, the styles "rex scottorum" (king of Scots) and "rex scotiae" (king of Scotland) were often used interchangeably.
The earliest styles applied to rulers in Scotland are primarily to be found in early Irish chronicles. To whit: we find descriptions of Scottish rulers in the Annals of Ulster (AU) and Annals of Tigernach (AT), which derive from the Iona Chronicle, a chronicle kept in Scotland. Other sources that name Scottish rulers are the Annals of Connacht (AC) and the Chronicon Scotorum (CS). In the early medieval period, the style that is most often given follows the pattern of "king's name, patronymic, title". So, for example, here is a list of Scottish rulers from the Gaelic chronicles; the source of the style is given in parenthesis after the name, patronymic, and title, along with the year within the chronicle (usually the year of the king's death). As a note, before the eleventh century, there was no fixed term for "Scotland" in Gaelic. Prior to the tenth century, the rulers of the area now comprising modern Scotland are either designated as being "of Picts", "of Fortriu" or "of Alba", standardising after 900; but the rulers of Moray, not by historiographical tradition called "King", are called king in the sources; moreover, they are sometimes called "kings of Alba". Note, "ri", "rig", and "righ" are the Gaelic words for "king".
"Pictish" Rulers
I can give you an explanation for France.
In 481 or 482, at the death of his father, Clovis became King of the Salian Franks. He then federated the Frankish tribes and invaded Gaul, become King of the Franks. At this time, the title of King (« Rex » in latin) is to be understood as the ruler of a tribe, of people. When at his death in 511 his kingdom his split between his four sons into four independant sub-kingdoms (Austrasia, Neustria, Burgundy and Aquitaine), his sons, as well as their descendants, did not call themselves King of Neustria, or King of Burgundy, but they called themselves King of the Franks. Because they were ruler of people, not of land in particular.
Over the centuries, the Kingdom of the Franks was reunited and divided many times between descendant of Clovis, and by the tenth century the title of King of the Franks became associated only with the ruler of the Western part of the kingdom.
In the 12th century, Philipp Augustus started to title himself King of France, in addition to King of the Franks. By doing this, he changed the source of the legitimacy of his kingship. He was no more ruler of the people, and accountable to them, but ruler of the land. This is not random at all, as all along his reign Philipp II reformed his kingdom to centralize the power, and his considered to be the first French King to put the basis of a state.
After the French Revolution and the Restauration, the kings titled themselves King of the French, again not a random thing, showing that they were accountable to the French people.
So you see that the choice of terminology is quite important. However, it is important to note that for High Middle Ages this not all clear cut, as some things are lost in translation.
I must add that my answer is very simplified, as I tried to answer specifically to the why of the different terminology in France.
Source : La France au Moyen Âge, Claude Gauvard. La France avant la France, Mériaux.