The French words for “whole rest” and “half rest” are “pause” and “demi-pause” respectively. I find this concept interesting, as the literal sense of “pause” means a brief stop in the action. The word “rest” suggest taking the attention away from the current activity to do something else, which is not what musicians do when encountering the upside-down hat symbol. No matter how many rests a orchestra brass player encounters, they still need to count or pay attention to the conductor, or at least to the music. Hopefully they don’t go off and have a nap (though I have a feeling that happened before…)
It’s the same with “quater-rest,” or “soupir” in French (literal translation of “sigh”). The quarter rest doesn’t exist to help one rest their fingers as a player, but to let the music breathe in order to create tension or release. Some could argue that it does exist in some cases to let a wind player breathe, to which I would say: “Exactly, to breathe as part of the action of playing, and again, not to lie down for a second!”
This is yet another example of how French speakers use more words in their common use of the language to make the most subtle of discernments compared to English speakers, with their efficient umbrella terms. The language with the most authority on the question, the Italian language, uses “pausa” for to designate a “rest.” And strangely, English’s cousin, German, uses “pause.” So…where does the term “rest” even come from?