Both sound natural and normal to me, and mean the same thing. I would probably use "at the moment" for someone I didn't know and "right now" for someone I did, but that may just be a personal quirk. You'll be fine using either one.
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Grammar GeekYou can also say (in American English, anyway) "She's not here just now."Does your suggestion mean the same with my examples. If not, what does 'just' mean in your sentence? Thanks.
AnonymousThe difference is "right now" means this specific instant; I am typing an answer to a question on EnglishForward at 11.23am January 5th. "At the moment" means a time period; I am playing football at the moment - I am thirty minutes into a ninety minute game. For your example; "she's not here right now" suggests she could be back soon. "At the moment" suggests she