Private key is just a random number in a very large set of numbers.
The random number can be represented by a seed phrase.
If someone has your seed phrase, they have your random number, and therefore they have your private key.
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IN BRIEF: A seed phrase is a collection of words that is used to access your cryptocurrency wallet.
NB. Seed-phrases are not cryptocurrency-specific. For this reason, they can be used across hundreds, so that one seed can actually be used to recover an entire portfolio of coins and tokens. Users with a single seed can create a seemingly infinite number of receiving addresses. Please remember also to never give out your wallet seedphrases for any reason: it’s private, it’s yours.
WHAT IS A HIERARCHICAL DETERMINISTIC WALLET:
HD wallets generally have a master key pair: an extended public key and an extended private key. This double structure solves the problem of users needing to generate their own keys for transactions, which has caused security issues, sometimes resulting in loss of funds. Unlike its non-deterministic predecessor, all HD wallet addresses can be generated from the master key, thus eliminating the need for storing multiple key pairs.
MY RECOMMENDED FURTHER READING:
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First, congrats to the explanation, it is really well structured and easy-to-understand. Just an advice from my side.
I would also include directly here just a few Radix-specific things (in one or two extra sentence):
- Length of seed phrase
- How to (and not to!) store it
- Raise attention to NEVER send it to anyone, even it seems if someone is from the official Team.
I think they are too important to miss out, even if the question is not strictly asks about them.