Provinces and Dioceses in the late roman empire contrasted with those of the church

To add my interpretation. Political and ecclesiastical ranks in the later Roman Empire:

A civitas or city state - usually based on a earlier tribe - was ruled by elected magistrates. In the fifth century an imperial official with the rank of comes "count" was appointed to supervise each civitas in the western Empire. A bishop was in charge of the parish clergy in each civitas, and a civitas later became known as a diocese.

A province contained several city states and was ruled by a rector or governor - governors had several different titles. The bishop of the capital city or metropolis of the province became the metropolitan or archbishop of the political province.

A group of political provinces would be a political diocese ruled by a vicar. A political diocese would thus be 2 political levels above a city state which would later become a ecclesiastical diocese.

The political dioceses were under the four praetorian prefectures ruled by praetorian prefects, which were thus 3 political levels above city states. The emperor of part or all of the empire would be above all the praetorian prefects within his territory.

In time the senior bishop, metropolitan, or archbishop within a large region would become known as the primate of that region. For example, the medieval Archbishop of Canterbury was the primate of England which roughly corresponded to the vicarate or political diocese of Britain.

I think that the four praetorian prefectures were so large that it is unlikely that there would be a primate for a territory equivalent to any of them, though I doubt that the area of every primate corresponded very closely to a political diocese.

Several senior bishops and archbishops became known as patriarchs by the 6th Century AD with some authority over the bishops, archbishops, and metropolitans of their areas. They were the bishops of Rome, Constantinople, Antioch, Jerusalem, and Alexandria.

So the political and ecclesiastical organization of the later Roman Empire would be:

Civil civitas and ecclesiastical diocese: Count and Bishop.

Civil and ecclesiastical province: governor and metropolitan or archbishop.

Civil diocese: Vicar.

Civil prefecture: Praetorian prefect.

Jurisdictions of ecclesiastical primates (if they existed yet) and patriarchs often differed greatly from the borders of civil dioceses and prefectures.

As noted in The Catholic Encyclopedia (published 1907 and now in the public domain and fully digitized) there has been a gradual change in the meaning and usage of the term diocese over nearly the past two millennia, as well as varied usage between those regions formerly part of the Eastern and Western Roman Empire respectively:

Originally the term diocese (Gr. dioikesis) signified management of a household, thence administration or government in general. This term was soon used in Roman law to designate the territory dependent for its administration upon a city (civitas). What in Latin was called ager, or territorium, namely a district subject to a city, was habitually known in the Roman East as a diœcesis. But as the Christian bishop generally resided in a civitas, the territory administered by him, being usually conterminous with the juridical territory of the city, came to be known ecclesiastically by its usual civil term, diocese. This name was also given to the administrative subdivision of some provinces ruled by legates (legati) under the authority of the governor of the province.
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On the other hand, the present meaning of the word diocese is met with in Africa at the end of the fourth century (cc. 50, 51, C. XVI, qu. 1), and afterwards in Spain, where the term parochia, occurring in the ninth canon of the Council of Antioch, held in 341, was translated by "diocese" (c. 2, C. IX, qu. 3). This usage finally became general in the West, though diocese was sometimes used to indicate parishes in the present sense of the word (see PARISH).