what is actually stored on a hardware wallet?

[Bitcoin]

what is actually stored on a hardware wallet?

My understanding is that:

1. Your crypto is on the public ledger under a public key.


2. Your Hardware Wallet stores your private key (which is used to prove your ownership of the public key/wallet).


3. You create a password to protect your hardware wallet (something more easily remembered than a full private key hash).

What I don't understand, is that when creating a hardware wallet you're given a "recovery phrase" of 12 words you have to write down to recover your wallet if it gets lost.

How is this any different than just writing down your private key on the same piece of paper and foregoing the expensive wallet? If you have to write down what is essentially your private key anyway what exactly is the benefit/point of a hardware wallet?

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