From above, hosseinimr93 is absolutely right. During the generation of keys and addresses from hierarchical deterministic (HD) wallets, the seed phrase is first generated using entropy and checksum process to generate seed words (the mnemonic or the seed phrase) which is used to generate the seed using key stretching function in which PBKDF2 stretches the seed phrase (or + including the passphrase) using 2048 rounds of hashing with HMAC-SHA512 algorithm. From the seed is the master private key and master chain code are generated. The master private key generates the corresponding master public key (using the normal elliptic curve multiplication process m * G).
The private key, chain code and index number are used to create the child keys.
To know more about seed phrase, keys and addresses, you can read these for it:
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05.asciidoc#pubkeyhttps://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04.asciidocThe child private key is what you referred to as private key.
There are one way functions which really make it impossible to use private key to generate the seed phrase but the seed phrase can generate the private keys. Know that your seed phrase, seed or your master private key can be used to access all your child private keys which can be used to access your coins and spend it. So know that your child private key can be used to access the coin stored on blockchain with its corresponding address. The reason all private keys (be it child private key or master private key) should be completely remain only known to you, because if known to an attacker, it can be used to steal your coins. So protect your seed phrase, seed, master private key and private keys.
Also know that you master public key can be used to know all the bitcoin connected to your wallet corresponding addresses, it can not be be used to spend but it can deprive privacy, so very good to also protect the master public key for privacy reasons. Only addresses are for the public.
A seed phrase is a group of 12 - 24 words, while a private key is a combination of 51 or 52 alphanumeric characters.
To be more specific, they are 12, 15, 18, 21 or 24 words. Any shorter than 12 like 9 words and below are not secure.