Sorry for the questions but I’m interested in Church structure & hierarchy…
So, when the word “pope” was first used in reference to the bishop of Alexandria and meant something like “Metropolitan” who wielded authority over nearby sees. And when the title (meaning “father”) later was applied to the Bishop of Rome, it meant in that case what it means today more or less… …
No.
There are plenty of Catholic sources that will say that the term Pope, as a term of endearment, was more widely used in the early church (I have even read somewhere that it was a generally applied to any priest, I don’t know how strongly that argument can be made), and later (late 11th century, after the great schism) became reserved to the Metropolitan of Rome in the west. I don’t think one will find any canons from the early days of Christianity on the subject of restricting the term, but I am interested to find out.
Anyway, the office of ‘Pope’ in the west, as the office of the bishop of Rome, has evolved. So of course the meaning of the term as we use it has also evolved.
Originally the bishop of Rome was a greatly esteemed Metropolitan in central Italy, but he did not have ordinary jurisdiction as far as Milan, for example (probably not as far as Naples either).
In modern days he not only has ordinary jurisdiction in Milan, he names the Metropolitan of Milan and all of Milan’s suffragan and surrounding bishops, codifies the canons for the church of Milan and regulates it’s liturgy, it’s calender, it’s monastic houses and it’s seminaries, and can remove anyone involved.
So there is a big difference over time.