According to the Gospels of Mark and of Matthew, the Sanhedrin wish to condemn Jesus to death, but they find the lack of evidence against him to be unhelpful. Matthew and Mark state that many false witnesses made statements to the Sanhedrin, including a claim that Jesus had said he would destroy the man-made temple, and replace it with a non man-made one three days later; according to Matthew and Mark the statements did not agree with each other, and hence since multiple witnesses are required by the Deuteronomic Code, the Sanhedrin are unable to condemn him by this.
The difference is that others had said Romans were the only ones with authority to condemn a person to their death.
The Sanhedrin has found Jesus guilty of the religious offence of blasphemy. This would be of no interest to the Romans, so the Jewish leaders have to change the charge against Jesus from claiming to be the Son of God to saying he is the King of the Jews. In doing so they are emphasising the political rather than religious implications of claiming to be the Messiah. The Romans would take action for a political offence, particularly something that posed a threat to Roman rule.
The latter was no-one wanted responsibility whether he lived or died and they gave the community a choice of one person could be voted to be freed and corruption from the priest freed one man but it wasn't Jesus.
The real difference were that the Sanhedrim Priests abused their position of power of Roman law and through abusing voice and influence of the community they acted and were corrupt. Other abuses were being above rights of humans that healed communities, including fellow preachers such as Jesus who was taken to trial twice due to the Sanhedrin actions. In a heartless manipulation of both crowds all knowingly that the Romans initial actions were of disinterest.
