A wallet is basically a device/SW that keeps an overview of your unspend transactions UTXO's and the private keys to be able to proof you are the owner of those UTXO's.
The while set of those UTXO's and PK's is derived from your unique set of characters.
That set of characters can be your set of seed words or a set of seed words extended with a passphrase.
The are all seeds, 12 or 24 words out of a predetermined list, with or without an extension of 1 to 128 characters...
For the deterministic wallet, we all use those, it doesn't make a difference:
A deterministic wallet is a system of deriving keys from a single starting point known as a seed. The seed allows a user to easily back up and restore a wallet without needing any other information and can in some cases allow the creation of public addresses without the knowledge of the private key. Seeds are typically serialized into human-readable words in a seed phrase. The BIP 0032 standard for hierarchical deterministic wallets is used by all good wallets as of 2019.
You left out an important detail. You do need more than just the seed phrase to recover funds from a deterministic wallet. The derivation path is also critical to locating your UTXOs. You can think of it as a treasure map to locate the funds. Without that, there’s a lot of guesswork required, and potentially lost funds if the wallet isn’t following a documented standard. It’s very important to note the type of software and hardware used to generate the wallet to avoid a panic situation where a wallet appears to contain no funds, when actually it’s just missing the instructions to locate them.
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