Neither is "President of the USA" found in the title "Leader of the free world"; House and Senate are not found in the term Congress; "Pope" is not found in the title, "Bishop of Rome". Different designations, descriptions, terms - can refer to the same person or group.
I believe that people a lot smarter than you and I have translated the Bible. Although Sanhedrin is not in the original Greek per Matthew 26:59, The priestly division managers, and the elders and the whole is. Many translators have determined that this group of Jewish leadership was the Sanhedrin. I know you disagree. Lets stop arguing the point.
Final word: Stop falsely labeling people who disagree with you. This is an Alinsky tactic that we should all avoid.