I'm not sure if this applies to all literature and whatnot, but I was reading the Licence to establish a colony in Virginia by King James I in 1606, and it mentions things like land "not actually occupied by Christian princes". I also see the usage of 'prince' for what seems to be a King in Hakluyt's appeal to Queen Elizabeth I. Am I just not understanding correctly? Am I wrong in thinking that they're Kings but in reality they're Princes? If so, were Princes historically given control of colonies? If they actually were referring to a King as a 'prince', how has English evolved to make Prince-->King?
In the early modern era, the term "Prince" also had a more generic meaning of "a ruler possessing some degree of sovereignty". In that sense, the ruler a small independent dukedom like Victor Amadeus of Savoy was just as much a "prince" as king James of Scotland.
It's in this sense of the word prince that Machievelli entitled his most famous work The Prince.
It must also be said however, that standards for what was considered a sovereign polity was not terribly consistent, especially in Central Europe and the HRE with its complicated mix of overlapping jurisdictions and small highly fragmented duchies and whatnot.