From what I understand, the Old Republic has existed in some form for a thousand generations, 25,000 years. I’m sure it has changed a lot, grown and shrunk, survived countless wars and conflicts. But the fall of the Old Republic basically was the near or total collapse of the Republic a thousand years ago, coinciding with the “destruction” of the Sith. After that war was over, the Republic was reformed (in Legends it was known as the Ruusan Reformation), which led to the creation of the Galactic Republic we see in the OT.

Based on the time period, you could say the “High Republic Era” was the golden age of the Republic. A Pax Republica. It’s the High Republic because it was the Republic at its best. I guess as conflicts have begun to arisen again leading up to the films, people saw the High Republic Era as over.