Both are same to my knowledge. One is the derivative of the other, so they are of the same importance.
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Just a small correction: the seed phrase is not derived from the private key (it isn't a reversible process). Instead, the seed phrase (in mnemonic format) goes through a conversion process from mnemonic to seed in hex format using PBKDF2 (with checksum).
The result is a hash sequence (mnemonic + passphrase (empty or not)) with 64 bytes, which is used to generate the master xpriv and, in turn, the child private keys.
Here is the LearnMeABitcoin site, which contains all the details on how an HD wallet works:
https://learnmeabitcoin.com/technical/keys/hd-wallets/mnemonic-seed/