In modern usage, they're both empty titles that no longer correspond to their historical meanings. But if you look at the etymology of the terms, a principality was clearly a political subdivision of higher status than that of a duchy. A principality is ruled by a prince or princess who is in line for the throne of the kingdom, while a duchy is ruled by a mere duke.

These are historically derived and have no real relevance today ; the titular rulers, if they exist, are figureheads whose role is ceremonial rather than constitutional. Not so in some countries though, and indeed the two titles can be held concurrently cf Prince William, Duke of Cambridge.

A principality is ruled by a prince and a Duke rules the other. A prince has higher rank than a Duke.

We found out that in the process of naming the countries, the British assigned them different statuses.