They probably would have understood if they thought it was something worth learning about - but it definitely wasn't interesting or important to them. Christians were Christians, and their doctrinal disputes made no difference to the Muslims whatsoever.

Here is a summary by Carole Hillenbrand:

"The medieval Muslim felt superiority and condescension towards Christians. For him it was indisputable that Christianity, an incomplete and imperfect revelation, had been superseded and perfected by Islam, the final Revelation, and that the Prophet Muhammad was the seal of the prophets. Such supreme confidence in the values that were based on this Revelation did not engender great intellectual curiosity in peoples of other faiths which were by definition wrong or incomplete. The Muslims showed little interest in Christianity, whether it was the Latin Christianity of the barbarians of western Europe, the eastern Christianity of their great enemy and neighbour, Byzantium, or the Oriental Christian communities who had lived under Muslim rule since the Arab conquests in the seventh century...They knew a certain amount about Christianity from the Christian communities in the Middle East, but even to those familiar groups they gave scant attention." (Hillenbrand, pg. 267-268)

Christians from Europe were generally called Franks ("Ifranj"), and Byzantine Christians were Romans from the land of Rome ("Rum"), but those were ethnic/geographical terms. Christians overall, wherever they were from, were "Nasrani" (Nazarenes, people from Nazareth, like Jesus). There were Christians all over the Muslim world, from Spain in the west to Central Asia in the east. Their geographical/ethnic origins were significant, but they were all Nasrani.

Was Jesus the same divine figure as God? Was Jesus fully human? Was Jesus fully human and fully divine at the same time? Does the Holy Spirit proceed from God and from Jesus, or just from God? These questions, among other things, are the source of all the differences between the various branches of Christianity, and were sometimes the source of violence and bloodshed. But they would never even have occurred to a medieval Muslim, and if they did, their reaction would have been "who cares?" Islam has its own understanding of Jesus, and any Christian understanding was incomplete/wrong, so there was no reason for a Muslim to investigate it. For Muslims, Islam had a much more refined understanding of monotheism, and these petty disputes among Christians were nothing more than evidence of Christianity's pagan, polytheistic nature.

I was reading about something similar the other day, when there was a question Mongol communication with Europe - that question was about a different subject entirely, but there were missionaries from Latin Catholic Christians Europe to the Oriental Orthodox ("Nestorian") Christians in Central Asia and China. In one case in 1254, there was a debate between a Latin (the missionary William of Rubruck) and an Orthodox Christian, as well as with a Buddhist monk and a Muslim. They argued the relative merits of their versions of Christianity, and then:

"The Nestorians prevailed upon the Franciscan [William] to stand down so that they could at last engage with the Muslims; but the latter refused to argue with them, conceding that everything in the Gospel was true...the statement could simply have reflected the fact that Muslims regard Christianity as an incomplete version of the revelation fulfilled in Islam – as being in some measure, therefore, subsumed within Islam." (Jackson, pg. 276)

I should note that from the other side, medieval Christians also had basically zero interest in Islam either. Thanks to the crusades, and missions like the one above to the Mongols, some Europeans did try to learn about Islam, at least for the purposes of debating with Muslims. But the vast majority of people didn't know anything about Islam, and they didn't care, just like most Muslims didn't know/care about the different kinds of Christianity.

Sources:

Carole Hillenbrand, The Crusades: Islamic Perspectives (Routledge, 1999)

Peter Jackson, The Mongols and the West (Routledge, 2005)