I always thought the Private Key was the 128 binary bits represented by the 12 Word Mnemonic or the 256 binary bits represented by the 24 Word Mnemonic.
I am working on an article about the Private Key and was doing some deep diving/research into it and now I'm realizing that I have been wrong all along. :=)
I'm beginning to understand that the mnemonic seed phrase simply represents the entropy used in creating the Master Private Key.  O.K.

So, I want this article I am working on to be accurate.  While I am not necessarily interested in giving an exact coding example I do want to have all the elements involved correctly identified and explain how they work together to create the Master Private Key.

It is my understanding that the 128/256 bits of entropy provided by the mnemonic seed phrase is hashed along with either a NULL STRING or the 2nd Passphrase provided per the BIP39 standard using HMAC-SHA512.  But I have seen references to a third static item of information that is either "Bitcoin seed" or "mnemonic" that is also hashed in there with the above two items I mentioned.  So which is it?  "Bitcoin seed"?  Or "mnemonic"?  Or is it something else?  Or have I completely lost it and don't understand anything?  :-(  And are all 3 items hashed together at the same time?  Or are there steps?  And if so what is hashed at each step?

I would like to know the exact sequence of events that occur when the wallet software accepts the mnemonic seed phrase and the 2nd phrase sometimes referred to as the 13th/25th word.  What steps occur to arrive at the 512 bits that represent the Master Private Key (Left 256 bits) and the Master Chain Code (Right 256 bits).  Also, is the Private Key just the LEFT 256 BITS?  Or is it the entire 512 bits?  Just trying to clarify things in my head.  Apparently I do not fully understand what the Master Chain Code is or what it does?  Maybe it's not important that I understand but if it involves the Private Key or affects it in any way then I would like to understand it better.  If not I am O.K. with explaining to the reader that the Master Chain Code while important is not part of the Master Private Key.

Thank you so much in advance for wading through my questions.  I really appreciate any light or clarification that you can shed on this for me.

Kresp.