Prinz and Fürst.
The fact is that a prince can be thought of as a cadet member of a royal house (e.g. Carl Philip of Sweden), the sovereign of a principality (e.g. Hans Adam II of Liechtenstein), a cadet member of a grand duchy (e.g. Felix of Luxembourg), a cadet member of a principality (e.g. Nikolaus of Liechtenstein), or a member of the high nobility (e.g. Konstanty Radziwiłł.
But in German, the use is more narrow, insofar as the sovereign of Liechtenstein or Monaco is certainly never referred to as PRINZ. Even in that language, however, the use of the term is probably not very restrictive, insofar as it likely is otherwise used in the same way as the term PRINCE in English. That is: with the exception of sovereigns, PRINZ can mean a variety of things.
In Spanish, however, the term PRINCIPE seems to be restricted to the heir apparent to the throne (Prince of the Asturias, the title by which King Felipe VI was styled, prior to his accession). All other cadet members of the royal family are styled with the title INFANTE -- albeit with the same qualification of Royal Highness.
Or am I mistaken in all this?