You can picture per diem as a measuring cup with only one mark on the side: ONE DAY. Whatever is being counted — work done, money paid, a charge on a bill — is poured out one at a time. Two days, two cups. Nothing is counted in hours and nothing is counted in months. Once you can see that cup, every use of the word is just a question of what is being poured into it: the hours you worked, the wage you earned, or the food money you are allowed to spend before the sun goes down.
「per diem」可以想成一個量杯，杯身上只刻著一條線，寫著「一天」。不管要算的是工作、薪水，還是帳單上的費用，都用這個杯子一杯一杯量出來。做兩天，就是兩杯。不用小時算，也不用月算。看得到這個杯子，剩下的差別就只是「這次杯子裡裝的是什麼」——是你上工的日子、是那一天的工資，還是天黑以前可以花掉的伙食費。
From the word’s history
Latin per (for each) + diem (day), taken into English whole, so the words still say exactly what they do: for each day.
拉丁文 per（每一）＋ diem（日），整組直接搬進英文。所以這兩個字到今天說的還是它們原本的意思：每一天。這也是為什麼它用起來永遠離不開「一天」這個單位。
Wiktionary, "per diem"
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