Difference betwn Sanhedrin and Anshei Knesset haGedola

Is there a difference between the Sanhedrin and the Anshei Knesset haGedolah?

The Sanhedrin and Anshei Knesset HaGedola are one and the same, just that in times where there were 71 members they're called the Sanhedrin, but after the aliya of Ezra, when there were 120 members, they're called by the longer name, until they went down to 71 again (as they died…).