I suppose the primary difference between a monarchy and a dictatorship is in terms of self-identification. We still have absolute rulers being monarchs, mind you. KSA and Qatar, amongst other Gulf states, still have very strong monarchies. What differentiates a monarchy from a dictatorship is self-identification. A dictatorship becomes a monarchy when the ruler drops all pretense of democratic rule and says "Yep, I'm the king now".

I assume you're thinking of North Korea? Hereditary succession isn't as common in modern dictatorships as you might think. Most modern dictatorships transfer power simply within the ruling party, not within the family, as it does in the DPRK. Think the Soviets with Stalin > Krushchev > Brezhnev. Also, monarchies are not necessarily passed on based on primogeniture. Most European kingdoms started out as elective monarchies; the nobles would choose a king from amongst them, best exemplified in Hungary, Poland-Lithuanian Commonwealth, and the Holy Roman Empire, and it was only later that primogeniture became the norm. Even the most classic examples of primogeniture, France and England, began as elective monarchies, although this quickly changed once each state managed to produce stable dynasties. Hell, technically the Vatican City is a monarchy; the Pope rules, and is absolute "Sovereign" over the Vatican City, and he's certainly elected. They are still monarchies, ruled by a king/duke/emperor, just that the monarch's title isn't hereditary. What this intends to show is that the definition of a monarchy isn't based on hereditary succession. So why isn't a dictatorship a monarchy? Primarily, a dictatorship will still maintain pretenses of democracy. North Korea still has a parliament (note: not incompatible with monarchy), its rulers are still nominally elected, and the Kims are just the leader of the largest and permanently installed party. Regardless of whether or not they are de facto dynastic rulers, they remain dictators until they choose to become kings.

This isn't a new concept, mind you. There are plenty of historical examples of what we would recognise as dynastic dictatorships without being monarchies. The de Medici family, for example, maintained de facto dictatorship (bar a few revolutions) of the Republic of Florence for almost a century before actually establishing the Duchy of Florence, thus making themselves dukes (i.e. monarchs). Then there's also the classical example of Rome; Rome's dictatorship was established by Julius Caesar, but he was not a monarch. It was only once his "son" Augustus established himself as emperor and dissolved the Republic (but not all its apparatus) that Rome transitioned to a proper monarchy.

I suppose technically there's no difference in terms of powers between a monarch and a dictator. However, the distinction between a dictatorship and a monarchy isn't anything new; it's always been there, as far as there have been democracies and monarchies to make the distinction relevant, and is certainly not a modern invention. The transition from a dictatorship to a monarchy has always historically been the dissolution of the vestiges of democracy, and formalisation of true monarchical status, neither of which has really happened in North Korea, or any other modern dictatorship, for that matter,.