Interesting. I have heard “running errands”. But I’ve never heard buying groceries being referred to as a “grocery run”.

(Then again, I mostly know English from the internet, so just because I never heard it doesn’t mean it doesn’t exist. If you don’t mind the question, which part of the world are you from?)

Edit: Never mind, turns out I was replying to someone who got banned from Lemmygrad for being annoying in a different thread. I’m still curious where that phrase is used, if anyone else wants to tell me.