JTI: There were two Clement VII’s. After the Great Schism, another pope came along and re-used the Avignon pope’s name as a demonstration that the former’s claim was illegitimate. Similarly, there was another Pope John XXIII in more recent times.
Here’s the timeline for the whole embarassing period. This is mostly taken from http://www.friesian.com/popes.htm
1305: The King of France uses his influence to get Clement V elected. Clement V moves to Avignon, France. For the next 73 years, the papacy is under the control of the French king. (It was Clement V who wiped out the Knights Templar, BTW.)
1305 - 1378: Clement V, John XXII, Benedict XII, Clement VI, Innocent VI, Urban V, and Gregory XI all serve as popes. This period is what Church historians call the “Babalonian Captivity.”
1378: Urban VI is elected pope. He tells the French king to go screw himself and goes back to Rome. Some French cardinals decide that they won’t accept this move, so they elect a new guy, Clement VII, who stays in Avignon. This is the beginning of the Great Schism.
1389: Urban VI dies. The cardinals in Rome elect Boniface IX pope.
1394: Clement VII dies. The Cardinals in Avignon elect Benedict XIII as their pope.
1404: Boniface IX dies. Innocent VII is elected by the Roman cardinals.
1406: Innocent VII dies. Gregory XII is elected by Rome.
1409: The Council of Pisa is convened to solve the schism. They elect a new pope, Alexander V. God only knows why they thought a third contender would make matters any better, but they did. Neither Greg nor Benny want to yield their claims to this new guy, so the Church now has 3 popes.
1410: Alexander V dies. The guys from Pisa elect John XXIII to succeed him.
1415: Everyone finally decides that enough is enough. The Council of Constance is convened to settle things permanently. Emperor Sigismund arrests all three claimants and forces them to resign (or abdicate or whatever). Martin V is elected pope in 1417. He goes to Rome and that’s that.
Gregory XII dies in 1417, John XXIII dies in 1419, and Benedict XIII in 1423. The guys in Avignon weren’t quite done, however. After Benedict’s death, they elected another new pope, named Clement VIII, but nobody seems to have paid any attention to him. He died in 1429.
In hindsight Clement VII, Benedict XIII, Alexander V, and John XXIII, and Clement VIII are considered anti-popes. Urban VI, Boniface IX, Innocent VII, Gregory XII, and Martin V are considered legitimate popes. As I’ve said, some of the anti-popes’ names have been re-used by latter popes as a sign of contempt.