What did “Africa” mean to an ancient citizen of the Roman Empire?
It seems as though the name means three or possibly four different but related things, and it’s helpful to sort them out carefully:
1. The province called “Africa.” This changes over time, because the Empire was always reorganizing its provinces. When the Latin Church Fathers say “Africa,” it means this more often than not. Often they specify “Africa and Numidia” to indicate that whole region.
2. Northern Africa outside of Egypt.
2a. Northern Africa outside of Egypt and Libya, so that to include all of northern Africa, the writer says, “Egypt, Libya, and Africa.” In this division, I think “Africa” basically means “Latin-speaking Africa.”
3. More or less what we mean by Africa today. The ancients didn’t really have our idea of a “continent,” but the world was divided into three parts, In Greek, the word “Libya” takes the place of Africa here. For example, in Eusebius’ Life of Constantine (Book III, Chapter 7): “In effect, the most distinguished of God’s ministers from all the churches which abounded in Europe, Libya, and Asia were here assembled” (namely, at the Council of Nicæa).
Sometimes we see the same writer using two different meanings in the same book.
Theodoret quotes Constantine’s letter about Easter: “I engaged that you would be ready to adopt it likewise, and thus gladly accept the rule unanimously adopted in the city of Rome, throughout Italy, in all Africa, in Egypt, the Spains, the Gauls, the Britains, Libya, Greece, in the dioceses of Asia, and of Pontus, and in Cilicia,…” [Ecclesiastical History, Book I, Chapter 9.] Here we have the division of northern Africa into Africa, Libya, and Egypt.
But later in the same book, Theodoret writes about Constantine’s success: “For this reason he was blessed with the special protection of God, so that although he held the reins of the whole of Europe and of Africa, and the greater part of Asia, his subjects were all well disposed to his rule, and obedient to his government.” [Ecclesiastical History, Book I, Chapter 24.] This is the division of the world into three parts, with Africa one of the parts, obviously including Libya and Egypt.