In the analogy we have three persons, lets call them John, Jim and Theo. John and Jim represent all men John represent those will go to heaven, which in this analogy is represented by going to the concert, of which a ticket, representing salvation, is required. Jim represents those who do not go to heaven while Theo represents God.
Monergism
John and Jim are not aware of the concert they even cannot afford to buy ticket no matter how hard they work. Theo decided to send free ticket to John. John found the ticket inside his mail box it made him interested in the concert and therefore he goes to the concert. Jim did not receive free ticket he cannot go to the concert and remains unaware of the concert.
Protestants and Bible only Christians who follow Calvinism or Reformed theology are monergists.
Synergism
John and Jim are not aware of the concert they even cannot afford to buy ticket no matter how hard they work. Theo took the initiative he offered free tickets to both John and Jim. John said he wanted to go to the concert and accepted the offer. Jim, on the other hand, said he is not interested in the concert and declined the offer.
Catholics, Protestants and Bible only Christians who follow Arminianism are synergists
Semi-Pelagianism
John and Jim are aware of the concert but they cannot afford to buy ticket no matter how hard they work. John decided he wanted to go to the concert. Realizing he will never be able to buy the ticket, he contacted Theo for help Theo gave him free ticket. Jim, on the other hand, is not interested to go to concert and does not bother to contact Theo.
Pelagianism
John and Jim are aware of the concert and they can afford to buy ticket, though they must work hard. John decided he wanted to go to the concert he has been working hard for it. Optionally he can ask Theo for help if he does Theo will give him money a gift from him (not a loan) and it can cover partial cost of the ticket. Jim, on the other hand, is not interested to go to concert and does not bother to do anything.
Pelagian and semi-Pelagian were condemned at Council of Orange in 529 AD.
Rome is basically Semi Pelagianism....
Salvation:
The Eastern Orthodox hold to synergism very, very strongly.