Byzantium was also, of course, "Roman" no less than the Italian peninsula. Constantinople, as everyone will know, became the capital of the Roman empire; old Rome was for a time a sort of rural backwaters with reduced population living in the ruins of what remained of the city.
Some Orthodox like Fr. John Romanidies insist the Orthodox are the true Romans and do not really like to refer to Roman Catholics as Romans or Catholics. The Frankish king Charlemagne only "became" a Roman emperor because the then pope -in the first act of its kind- anointed him as such. According to Fr. John Romanidies admittedly controversial account the Franks killed executed most of the Orthodox bishops, installed Frankish military leaders as the new bishops, made serfs of the Orthodox populace, and within a couple of centuries secured a Frankish papacy http://www.romanity.org/cont.htm
e.g. Fr. John Romanidies section 3. Franks, Romans, Feudalism, and Doctrine
. Without controversy (i.e. as one can learn from any major contemporary historian) it was especially during his reign that unprecedented animosity (e.g. replacement of rudeness for former respectful court-language in official correspondence from the West) developed in the West. It was also in Charlemagne's court that the Filioque was given an extreme emphasis. During the rule of the Franks we find a sudden upsurge in specifically racial animosity -anti-Greek/anti-Byzantine- among the Franks, as you can also read in R. W. Southern, Western Society and the Church in the Middle Ages
(before Charlemagne it was common to find popes of Rome with Greek names). The Frankish intellectuals -they imported salaried intellectuals from all over the world to work on religious historiography and theology- also set a number of specific agendas in terms of scholastic and legal takes on theological themes that continued to set the tone and content of theology throughout the middle ages in the West. Everyone mostly knows of the proliferation of forged letters, decrees, donations, histories, etc. to bolster Western claims which appeared at a near exponential rate in the West beginning after this time.
Latin can and often is used in the phrase "Latin Catholicism" in the sense of Latium, i.e. ancient Rome without any sense of disparagement whatsoever in mind, though, and a contemporary Roman Catholic shouldn't, I think, assume the worst when the phrase is used.