Picture a room where the question is not what to do next, but whether these people still stand behind one person. Everyone has to say so openly, and the count decides whether that person keeps the job. That is the picture the words carry: support made public, counted, and costly to give.
Two branches
制度裡真的投的那一票
這是字面上的用法：真的開會、真的投票、真的有票數。
noun · B2
A formal vote held in a parliament or other official group, so that the members can show whether they still support the leader or the government. Losing one normally means the government has to step down.
信任投票
沒有投票，但做出來的表態
把投票那個畫面借過來用：沒有票匭，但那個動作一樣公開、一樣要付出代價，所以一樣算數。這是比喻上的延伸，字本身沒有換過來源。
noun · B2
Something you do or say that clearly shows you trust someone or believe in what they are doing, even though no real voting happens.
信任的表現