I haven’t seen him yet = I have not yet seen him, or I have not seen him. I haven’t seen him recently = It has been a while since I last saw him, but I have seen him. Both are correct.
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AnonymousI haven't seen him yet.~ I'm expecting to see him, but so far it hasn't happened.
AnonymousI haven't seen him recently.~ During the time immediately preceding the time when I say this, there are no cases of my seeing him.