In Latin, is there an “adjective form of nation name” vs “of nation name” distinction?
In English we can say “Church of Rome” or “Roman Church”, or “Embassy of Germany” or German Embassy”, or “Prime Minister of Israel” or “Israeli Prime Minister.” From google searches and browsing grammar text books I cannot determine the difference between the two forms, the meaning of the two, the name of the distinction, or its significance.
In Latin is there a similar syntactical difference and if so what is its significance?
For example, how would we translate “Patriarch of Alexandria” and “Alexandria Patriarch”? Or “Catholic Church of France” and “French Catholic Church”? Or “Army of Serbia” and “Serbian Army”?
Edit: cnread answered a previous question by saying: “ Latin doesn't typically use a genitive for expressions such as 'the island of Sicily' or 'the city of Rome.' Instead, it tends to treat the two nouns as noun + appositive, much as it would for phrases such as 'the consul Cicero', where 'the consul' and 'Cicero' refer to the same person.”
But in the case of my question the Patriarch and Alexandria do not refer to the same thing. There is a relationship of dependence. So we use the genitive.
Does that mean that Both Patriarch of Alexandria and Alexandrian Patriarch are both translated “Patriarchatus Alexandrinus”? And Catholic Church of France and French Catholic Church are both translated “Catholica Ecclesia Gallicana”?
The question is about whether the two ways of expressing it in English should be translated in only one way in Latin?