And as a secondary question, was there an intermediate period where only the Heir Apparent would be styled prince or something?
hi! a direct response to your questions is very welcome, but fyi, there have been several questions about the meaning of "prince" in this sub, so you may be interested in checking these out
I'm not an expert, but I do know that some countries preferred the term "principality" to "kingdom". The prince was a king in all but title, and often did this to show humility and piety. A good example is the Principality of Antioch.