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Is it a 1-to-1 relationship? If so, does that mean they are interchangeable? Can I then store just one of them and derive the other when needed?

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It's the same relationship between the branches of a tree and the seed you put in the earth that grows into that tree.
We have a seed that can be used to derive child branches and child keys which makes the relationship is one directional (you can always derive the child key by having the seed but you can't compute the seed from the child key).

Take a look at the following picture from BIP32:
enter image description here

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  • Thanks! So, all in all, to start using Bitcoin, I can pick a random seed phrase. Then I can generate several private/public key pairs. That's what these software wallets do.
    – m_ocean
    Commented Mar 31, 2021 at 6:05
  • Essentially. Almost all wallets are deterministic these days. They create a random seed which they use to derive all the future keys. That way they only rely on RNG once. Commented Apr 1, 2021 at 10:34

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