[ithkuil]

Prince is the son of a monarch. A monarch is the sole ruler (mono = one).

In an oligarchy you can still have powerful military rulers "whose chariot wheels roll everywhere"

To continue the comparison with the Roman republic. Consuls where great leaders bestowed with great power and honoured for their military successes. The Roman republic had a taboo of monarchy, one that Caesar himself played with dangerously and which got him killed.

[denton-scratch]

Yabbut in some circumstances, a "prince" is effectively a king. I'm thinking of the princes in the Holy Roman Empire; they paid fealty to the Emperor, formally; but they were the masters of all they surveyed. And the word "prince" in literature often seems to mean exactly the same as "king".

[argentier]

Princes are not necessary the sons of monarchs: independent principalities can and do exist (see for example Monaco).

Prince comes from princeps (the first), a title used by the Emperor Augustus.

[ithkuil]

Well if we want to dig in the etymology then princeps meant the first in the order (in battle) of the soldiers. This was used during the Roman republic and the connotation was indeed that the first soldiers were the best, more experienced ones Over time Romans realized that it was more effective to not deploy their best soldiers first and so the princeps (the best most experienced soldiers) were in the back.