I've sometimes heard it said that people - say in the middle ages - didn't think of "progress" the way we do (e.g. we'd say that women's suffrage is a historically important event because it's progress), so I'm wondering what kind of framework they did use to understand their own history.
For example, medieval monks were aware that Aristotle couldn't possibly have been Christian, but did they see this as a sign of a profoundly different society from theirs? And if so, how did they frame the process of getting from Aristotle's world to their own? Or did they conceive of Ancient Greece as a broadly similar world to theirs only pagan? In the other direction, would a forward-thinking monk hold the conviction that certain profound changes in society were desirable to make it somehow better? Would they have thought of such changes as historical processes?
Sorry if the question is a little vague, I'm having some trouble phrasing it.
Western European intellectuals with a clerical background during the Middle Ages were deeply influenced by traditional Judeo-Christian thought whenever they dealt with the past. In general terms, this meant that that they perceived human history as series of events which had a definitive beginning (creation), stood under a divine promise (salvation), and had an ultimate goal (last Judgement).
In contrast to pagan scholars in classical antiquity, medieval historians therefore did not perceive history as cyclical anymore. Insofar, they had a sense of progress. However, this progress lay in the hands of God who had his own plan. Since Constantine the Great, the Roman Emperor was perceived as being part of that plan because he was the first ruler who had officially professed his faith in the Christian God. This was part of the reason why monarchy and especially the so-called Emperor of the Romans in the HRE were eventually legitimized by the grace of God during medieval times.
Regarding the relationship to classical authors, Christian historians and theologians had become aware of the problem that there were “two histories” (Christian and pagan) since late antiquity. The Greek historian and bishop Eusebius of Caesarea (-339/340) tried to solve this problem by parallelizing the Old Testament with classical historical texts by authors like Livy. For the Latin West, his works were partly translated by Jerome.
The fact that the Western Roman Empire was threatened and eventually fell during the 5th century was of course another great problem for Christian historiography since the end of antiquity. However, Orosius, a student of Augustine, interpreted world history with a concept of succeeding empires (Babylon, Persia, Greece and Rome). This notion, translatio imperii, was inspired by the Book of Daniel in the Old Testament. It was widely used by medieval historians in the Holy Roman Empire such as bishop Otto of Freising (ca. 1114 - 1158) to interpret their own times. For historians like Otto, this meant that as long as a “Roman” emperor ruled, the imminent end of the world was postponed. From their perspective, change and “progress” thus could be perceived as signs of the end times.
As for their image of ancient times, it is most likely true that mediaeval historians perceived them as “broadly similar to their own” as you put it. Looking at the miniatures/illuminations produced for Otto’s Historia de duabus civitatibus, a world history from creation until the Last Judgement, one can see how people in ancient times, such as Caesar, were depicted with medieval outfits and weapons: Cod. Jenensis Bose q. 6, fol. 20v