Hold one picture: something that should run smoothly catches for a moment, makes a short sound, and then goes on. In the body that is the breath — one sharp 'hic' you did not choose and cannot stop, usually a run of them, and then they are gone. Everything else this word does is that same catch, lent to something bigger: a plan, a deal, an engine, a video call.
Wiktionary derives hiccup from earlier hickop / hicket, from hic (imitating the sound) plus the small-thing ending -ock. The word is a copy of the noise it names, which is why the sound sits at the centre of every use.
來源記載 hiccup 來自更早的 hickop、hicket，由 hic（模仿那一聲）加上小詞尾 -ock 組成。也就是說，這個字本身就是那個聲音的複製品——所以每一種用法的中心都還是「短短的一聲頓挫」。
Wiktionary entry for 'hiccup' (kaikki extract, source_ref kaikki:3f6f69a190036ae4:426453165:79560)
Two branches
身體發出的那一下
這一族就是核心畫面本身：呼吸突然卡住、發出一聲、擋不住。名詞講那個聲音，動詞講那個動作。
noun · B1
A sudden short sound in your throat, made when your breathing stops for a moment without you meaning it to, often after eating or drinking too fast; usually used in the plural for a run of them.
打嗝（呃逆）
事情或機器卡了一下
同樣的頓挫搬到身體以外：本來該順順跑的流程或機器，突然斷一下、再接回去。因為打嗝很短又會自己過去，這個字就帶著「小、而且會好」的分寸。
noun · B2
A small problem or short delay that stops something going smoothly for a while, but that does not change how it finally turns out.
小狀況；小插曲