Prince, like Duke, borrows its title from a Latin root with its own long political history: princeps, meaning first, was the term Augustus and his successors preferred for their own novel position as head of the Roman state, first citizen rather than king, a studied avoidance of a title Romans still associated with the overthrown monarchy. Medieval and early modern Europe narrowed the word considerably, using prince mainly for a ruler's son or for a sovereign ruling a smaller territory than a full kingdom, and it is this narrower, more junior sense, a commander of real standing but still beneath a king, that the grimoire catalogue adopts for its own ranked spirits.
Vassago, third in the standard Goetia sequence, is among the better known spirits carrying the Prince title, and like most Princes in the list he is credited with his own subordinate troops of lesser spirits, distinguishing the rank from a Duke's more variably sized command mainly by degree of seniority rather than by any difference in the kind of authority each title is said to carry within the catalogue's own internal, entirely human-derived logic of precedence. Other Princes in the list, such as Orobas and Seere, are credited with particular specialities, honesty in answers and swift travel respectively, showing that within the rank real differences of stated function persisted even where the catalogue's formal hierarchy treated them as equals in seniority.
Sources Lemegeton Clavicula Salomonis (The Lesser Key of Solomon)Anonymous (unidentified compiler) with Encyclopaedia Britannica (online academic reference)Encyclopaedia Britannica editors