Ttyjukl

In Harry Potter and the Chamber of Secrets, Tom Riddle is interested to know how Harry survived Voldemort's spell. This implies that Tom Riddle from the diary could not deduce/guess what happened that night.

The strange thing is that in Harry Potter and the Goblet of Fire, Voldemort seems to know exactly how the spell backfired (while this process has only taken a few seconds)*. Since Tom Riddle could not guess the cause, it's very unlikely Voldemort could work out this magical challenge himself.

Since the diary was destroyed after Harry's encounter with Tom Riddle, there is no way Voldemort could have learned what Harry told Tom in the chamber. Does this mean both "identities" share a memory and that Voldemort simply has access to the knowledge Tom (from the diary) accumulated at Hogwarts? If not, how did Voldemort work out why the spell backfired?

Does diary Riddle share memories with the “real” Voldemort?

I don’t think so. Voldemort is unaware that his horcruxes are being destroyed (implying he has no psychic connection to them).

Also, as I explain in my answer to How did the diary horcrux know about recent events?, the diary Riddle seems to have a third-hand and incomplete account of the events of Godric’s Hollow. That’s only possible if it’s not sharing memories with the real Voldemort.

How did adult Voldemort know that Harry survived if diary Riddle did not?

There are several factors which give adult Voldemort an edge:

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  Adult Voldemort has a spy close to Dumbledore.

  
  
  

  With Crouch Jr impersonating Moody, an old and trusted friend of Dumbledore, it’s quite possible he’s learnt Dumbledore’s theories about Harry’s survival, and passed them to Voldemort. By contrast, diary Riddle only has Ginny’s accounts, and she doesn’t know anything useful about how Harry survived.

  
  


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  Voldemort witnessed his defeat; Riddle only heard the aftermath.

  
  
  

  Again referring to the quotes in another of my answers, Riddle’s account of Godric’s Hollow is based only on Ginny’s retelling. She doesn’t know that Lily cast herself between Voldemort and Harry, or the exact sequence of events. Without that information, it may be impossible for Riddle to work out what happened.

  
  


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  Voldemort has about forty extra years of accrued knowledge and wisdom.

  
  
  

  It’s very possible that he only learnt about the magic of sacrificial protection after he left school. It’s an extremely rare and poorly understood branch of magic (and not one the teenage Riddle would have been actively seeking out). Since the two of them don’t share memories, it may be that teenage Riddle just doesn’t know enough to put the pieces together.

  
  
  

  (Forty: the Chamber of Secrets was last opened fifty years before Harry’s second year. Voldemort was defeated twelve years prior to that, so about forty years between horcrux creation and destruction.)

  
  


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  Voldemort knows what happened in Philosopher’s Stone.

  
  
  

  When Quirrell tries to touch Harry, he gets a nasty surprise:

  
  
  

  
  

  Harry’s scar was almost blinding him with pain, yet he could see Quirrell howling in agony.

  
  
  

  “Master, I cannot hold him – my hands – my hands!”

  
  
  

  And Quirrell, though pinning Harry to the ground with his knees, let go of his neck and stared, bewildered, at his own palms – Harry could see they looked burnt, raw, red and shiny.

  
  
  

  — Philosopher’s Stone, chapter 17 (The Man with Two Faces)

  
  

  
  
  

  This is another detail which could be useful in working out why Harry is protected, to which Ginny wouldn’t be privy. She knows he defeated Voldemort, but not how.

  
  

An additional possibility that @alexwlchan's excellent answer didn't mention:

Diary Riddle is many years younger than Voldemort was when he killed Harry.

Surely, a magician of the prodigious skill and intellect like Voldemort would learn new things in the intervening decades.

It's not at all implausible that he only learned about the sacrificial protection magic after the age when he made the diary (which was while he himself was still in Hogwarts, as it was made with Moaning Mirtle's murder when the Chamber was last open.

This is pretty confirmed by Voldemort's own words in Goblet of Fire

Voldemort raised one of his long white fingers, and put it very close to Harry's cheek. 'His mother left upon him the traces of her sacrifice – this is old magic, I should have remembered it, I was foolish to overlook it – but no matter. I can touch him now.'

If he can detect traces of the magic, it means he likely learned about the magic as a wizard, not second-hand from a diary-Riddle or from Barty as dry fact.

when Ginny 'pours her heart into the diary' she talked about Harry endlessly and would've touched on the subject that he survived Voldemort's killing curse. Leaving Riddle to believe there was maybe another Dark Lord about and he of course would have wanted to know everything Ginny knew.

I don't see any evidence in the books that Voldemort would share memories with the diary. In Goblet of Fire, Voldemort has (as has been have pointed out) time, experience, and resources unavailable to the teenage Tom Riddle, so his knowing things that the diary wouldn't know makes a lot of sense.

Voldemort is undoubtably connected to his living horcruxes (Harry and Nagini) but as he doesn't even recognize that Harry is a horcrux, that connection isn't straightforward. One can literally be directly in front of him and he isn't aware of it. So it seems unlikely that he would have access to the memories from Tom Riddle's diary.

@alexwchan

"I don’t think so. Voldemort is unaware that his horcruxes are being destroyed (implying he has no psychic connection to them)." Well you are wrong in this assumption because when "Some" of his horcruxes like Ravenclaws Diadem were destroyed Harry and Voldemort both felt it.