The Republic was founded many millennia before the Battle of Yavin, approximately 25,000 BBY, around the same time as the Jedi Order. In addition, the term High Republic denoted the era in which the Republic reached the zenith of its power from 300 BBY to 82 BBY.
Old Republic was a term affixed to the pre-modern Republic that existed until 1032 BBY, and the modern Republic that was supplanted by the Galactic Empire in 19 BBY. The Galactic Republic, also known as the Grand Republic or simply as the Republic, was a democratic union comprising thousands of star systems spread across the galaxy. ' The Galactic Republic was the Republic of legend, greater than distance or time.' ―Janyor
