The term "prince" (the female form is "princess"), from the Latin root ''princeps'', when used for a member of the highest aristocracy, has several fundamentally different meanings — one generic, and several types of titles.
The Latin word Princeps, kin to "primus" and "first among equals", was established as the title of the more or less informal leader of the senate some centuries BC. Emperor Augustus established the formal position of monarch on basis of principate, not dominion. He also tasked his grandsons as summer rulers of the city when most of the government were on holiday in country or attending religious rituals, and for that task, granted the title Princeps.
In Latin-based languages, Prince has two basic meanings: it could be a substantive title and a courtesy title. Substantive princes are in some cases reigning monarchs, and in some cases heads of their noble house. Courtesy princes may be members of a royal or a highly noble family, sharing their title with several relatives in similar position. Many other languages have (at least) two separate words for these two distinct meanings.