Back when collars and cuffs were disposable items too, speaking “off the cuff” meant something literal as well as metaphorical. I’m too young to remember that, but my mothers white jacket went off to be boiled between uses, and she’d write notes on her cuff even then…
My anesthesiologist told me that he’s sometimes had to pointedly explain to co-workers that a conversation between an anesthesiologist and patient isn’t a conversation other friendly people can join.