Picture a ring of material sitting high on someone's upper arm, above the elbow, where a whole room or a whole field can see it. The arm is the part of you that moves and points, so anything tied there travels with you and stays in view. What the band is made of decides what it does: cloth up there carries a message to other people, and plastic full of air up there carries you in the water.
From arm plus band. The word names a place on the body and a shape, and nothing else, which is why one word covers two very different objects.
就是 arm 加 band。這個字只講「位置」和「形狀」，沒有講功能——這正好解釋了為什麼同一個字能蓋住兩種完全不同的東西。
Wiktionary entry supplied in this packet (source_ref kaikki:3f6f69a190036ae4:996306195:20435)
Two branches
給別人看的那一圈布
用上臂「顯眼」這個特點：把身分或心情掛在最容易被看到的地方。
noun · B1
A band of cloth worn around the upper arm to show other people something without saying it: that you have an official job at an event, that you are the captain of a team, or, if it is black, that someone has died.
臂章；袖章
把人撐起來的那一圈氣
同樣是上臂那一圈，只是裡面灌了空氣：它的工作從「告訴別人」換成「托住自己」。這不是比喻，是同一個形狀被拿去做別的事。
noun · B1
One of a pair of plastic bands filled with air that someone, usually a child, wears around the upper arms to stay up in the water while learning to swim.
充氣臂圈（游泳用）