In Latin, is there an “adjective form of nation name” vs genitive “of nation name” distinction?

Question

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?

Answer 1

I'd like to begin with a quotation:

nec miserae prodesse in tali tempore quibat,
quod patrio princeps donarat nomine regem;

— Lucretius, De Rerum Natura I.93

This is about the sacrifice of Iphigenia by her own father, king Agamemnon, in order that the gods might grant the Greeks a swift journey to Troy. It can be translated as follows, where I have rendered the words in bold very literally:

"Nor could it benefit the wretched girl at such a time,
that she had been the first to confer the fatherly name upon the king;"

Does this make sense to the modern reader? Perhaps not. What is this fatherly name, and why did Iphigenia confer a name upon king Agamemnon?

Somewhat less literally, another set of options would be, "a/the name of a/the/her father" (articles are not used in Latin, and possessive adjectives are optional, as well as demonstratives). What is the name of a father? Is this intelligible?

Yet another translation is possible, which is even farther removed from the literal English translation:

"Nor could it benefit the wretched girl at such a time,
that she had been the first to confer the name of 'father' upon the king;"

Ah-hah, she was his firstborn child, so it was she who had made Agamemnon a father: but not even this fact could prevent him from sacrificing her. Now it makes sense.

It can be seen that the Latin uses an adjectival word (patrius, "fatherly") where I believe most modern languages would have used a genitive construction with a noun ("of father"). In Latin, this is also possible: nomine patris, literally "the name of father / father's name", from the noun pater "father". The ending -is signifies a genitive, "of father / father's".

But the Romans often preferred an adjective where we would use a genitive/possessive noun, as suggested in your Question. Each language has several ways to express what we call 'possession', as well as several types of possession (my father: strong relationship; my bicycle: ownership (actual possession); my leaving you: agent; etc.).

Each language has its preferences, possibly also depending on the type of of 'possession'. For example, in Latin, amor patris, literally "love of father / father's love", normally means "the love for (my) father"; whereas, in English, "the love of my father / my father's love" normally means "love felt by my father (towards me?)".

In many cases, though, there is probably little difference in meaning between adjective and genitive noun in Latin, just as there is little difference in English, but Latin just prefers the adjective in more situations.