What is the difference between Sanhedrin and Kenesset Hagedola?
Factually, Knesset Hagdola was the Supreme counsel during the Babylonian exile and sometime after, during the beginning of the second Temple. Slowly the number dropped from 120 to 71, which equals the 70 of the Elders mentioned everywhere in the Torah.
Since the mid-second Temple, the era of Zugot, the Supreme Court of 71 was given the Greek name of Sanhedrin. This court is Biblically mandated (Sanhedrin 2a, from Bamidbar 11:31), but it was not called the “Sanhedrin” until the second Temple era.