The Roman Empire, formed in 27 BCE, when Augustus declared himself Emperor of Rome, underwent a split in the late third century that created two distinctly different Romes: Western Rome, with its capital at Rome, and Eastern Rome, a Greek-speaking territory with the capital at the newly named Constantinople. Over time, these halves of the Roman empire took on different characteristics. When Western Rome fell to the Goths in 476 CE, eastern Rome continued. Western scholars named it the Byzantine Empire.
Eastern Rome continued as a feudal Empire until its long decline from the Crusades to its final end at the hands of the Seljuk Turks in 1453 CE. As Constantinople transitioned from a Christian city to a Muslim city, the lands that were once known as the Eastern Roman Empire became the Ottoman Empire
Once Constantinople fell, the Ottoman Empire began, and thus one gave rise to the other. Because Eastern Rome was culturally and politically different from Western Rome, as referenced above many Western scholars relabeled this as the Byzantine Empire, so it is easy to assume that Rome ended in the classical period. However, Roman rule was continuous throughout the post-classical period in the form of the Orthodox, feudal, Byzantine Empire, and only fell with Mehmed's siege of Constantinople in 1453.