It is convenient to think of important historical realms as consisting of several roughly concentric roughly circular areas or zones with the ruler have the greatest amount of power and authority in the innermost circle or zone and gradually diminishing amounts of power and authority in successively outer circles or zones.
Such an image may be considered very schematic and in real life areas that were part of one zone would often be mixed up together with areas that were parts of other zones. Some geographic areas might be parts of two or more zones at the same time and some geographic areas might pass from one zone to another zone from time to time.
Note that in many geographic areas a ruler might be his own boss and his boss's boss and so on.
So in the case of the Holy Roman Empire the Emperor of the Romans would have the most power and authority in castles, palaces, buildings, farms, estates, forests and other properties he was the private owner and lord of. Many emperors had vast private properties in various areas, both hereditary properties and properties belonging to the office of emperor.
The next zone would be the zone of the various counties the emperor was the hereditary count of, where he had many military and fiscal and political powers and rights over the other landowners.
The third zone would be the various duchies that the emperor might be the hereditary or other duke of, where he had a degree of powers and rights and authority over the various counts of counties and over any territories that were not part of any county.
The fourth zone would be the various kingdoms the emperor was king of, where he had a degree of powers and rights and authority over the various dukes, and counts, and lords, and abbeys, and bishoprics, and archbishoprics, and free cities and other political entities.
King Otto the Great of the East Franks or Germany, and of Italy or Lombardy, was crowned Emperor in 962 AD. In 1032 Emperor Conrad the First (usually called Conrad the Second because he was King Conrad II of Germany) became King Conrad the Second of Burgundy or Arles.
Since then the offices of King of Germany, King of Lombardy, and King of Burgundy, were united with the office of Emperor of the Romans. The emperor usually just used the imperial title. In the late 15th century the diet of the empire, composed mostly of German lords, began using the expression
Heiliges Römisches Reich Deutscher Nation,
which may mean "the German Nation of (belonging to) the Holy Roman Empire" but is usually translated as "the Holy Roman Empire of the German Nation" and in any case was not used nearly as often as many sources imply. Maximilian I, the King of the Romans since 1486, may have been annoyed by that phrase since in 1508 he took the title of elected Emperor of the Romans and King of Germany, distinguishing between the Empire and Germany, followed by all his successors.
Emperors did use the titles of king of various kingdoms outside of the three imperial kingdoms of Germany, Lombardy, and Burgundy they became the hereditary kings of from time to time. Note that for a time the kingdoms ruled by the Emperor included a claim to rule all of North and South America west of Brazil, as well as actual control of a large part of the Americas. The later emperors were almost always the hereditary kings of Hungary and Bohemia.
The fifth zone would be various kingdoms that belonged to the Empire at different times, a zone that largely overlapped with the kingdoms that various emperors became hereditary kings of. For example Bohemia was part of the empire since 962. Emperor Henry III (IV) made Duke Vratislaus II king of Bohemia for life in 1085. Emperor Frederick I appointed Duke Vladisalus II King of Bohemia in 1158. The royal title was not used from 1172 to 1198, when Premysl Ottokar I resumed it and it was confirmed by Philip and by Frederick II in 1212. The Kingdom of Bohemia remained part of the empire until 1806.
Other kingdoms which were tributaries or vassals or otherwise under the Emperor for centuries, decades, or years included Burgundy (before the Emperor became the king in 1032), Denmark, Poland, Hungary, England, Cyprus, (Lesser) Armenia, and the Eastern Roman Empire.
The sixth zone also largely overlapped with the zone of kingdoms that various emperors became hereditary kings of. That was the zone where some people taught and believed that the Emperor of the Romans was the rightful ruler of everyone and everywhere in the world. That zone included all European Christian areas, but Eastern Orthodox Christians believed that the Eastern Roman or Byzantine Emperor was the rightful ruler of the universe while Catholic Christians believed that the Holy Roman Emperor was the rightful ruler of the universe.
So the sixth zone would sweep in a board arc from Croatia and Bosnia through Hungary, Poland, the Grand Duchy of Lithuania, the Lands of the Teutonic Knights, Finland, Sweden, Norway, Iceland, Ireland, Scotland, England, France, Spain, Portugal, and the islands of the western Mediterranean.
The seventh zone would include all the lands which the Holy Roman Empire could claim to rule, overlapping and including all the previous zones. It would include all the regions ever previously ruled by any version or incarnation of the Roman Empire, plus all lands ruled or inhabited by Christians because of the special Christian duty to "Render unto God that which is God's, and unto Caesar that which is Caesar's", and also all lands ruled or inhabited by Christians or members of any other religion because of the pre Christian pagan Roman ideology that all persons everywhere were rightfully subjects of the Roman realm.