From ErfWiki

Proposed Canon

"Prince" and "Princess" are Royal titles for the popped "descendants" of Kings and Queens. Not all Princes and Princesses are Heirs, though all Royal Heirs are Princes or Princesses.

Known Princes and Princesses are:

• Prince Ansom (Heir; Former; now claims no royal title)
• Jillian Zamussels (Heir; Former; now Queen)
• Don King's son and daugher (Heirs; Former; both croaked)
• Prince Tramennis, son of King Slately, brother of Ansom. (Non-Heir)
• Prince Ossomer, also son of King Slately and brother of Ansom. (Heir status unknown; Former; likely claims no title)
• Additional Jetstone Prince, son of King Slately (status unknown)

Speculation

"Prince" and "Princess" could be honorifics for all Royal units (or merely all Warlords or Commanders) popped to a side ruled by a King or Queen. or A random percentage of Royal units popped on a Royal side might have the "quality" (like being Heavy) of being a Prince. (Since units popped by Royal sides have a random chance of being Noble or Royal, this might be another "step" up that ladder.)