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Once has a different meaing in these two, doesn't it?
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Comments  (Page 3) 
iasadihTo complement such a sentence, it should be sufficient to presume a question it may answer:-Are you and Jack well acquainted?-I have seen him once at a party.
The simple past has to be used here. The present perfect sounds very odd for a once-off event, unless you are trying to remember the event, and groping in your brain for the memory.
- Are you and Jack well acquainted?

1) Not really. I saw him once at a party about a year ago.

2) Not at all. I may have seen him once at a party, but that's all.
Okay, in case anyone has reached that far,

I have only seen him once (one time).
I once (=there was a time when I) saw him laugh behind her back.

In the above sentences, once means different things. That's what I meant from the beginning, but proposed examples of sentences which did not sound very natural.

Thanks everyone.
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iasadihI have only seen him once (one time).I once (=there was a time when I) saw him laugh behind her back.
I completely agree with your paraphrases.

CJ
CalifJim, I finally forgot to credit you for this answer, sorry.

Yes

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