Clarifying what it means to "transfer BTC to Ledger" or "store BTC on a cold wallet"

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I'll make it very short but this language shortcut is IMO rooted in a misconception of what a cold wallet really is. You can't transfer BTC to a ledger!

All BTC are in the blockchain, none are living on a wallet. What you can do though is proving the ownership of your BTC by signing a transaction. To sign you need what we call the private key. It is so unlikely that you anyone can find the private key corresponding to a public key (in short your address) that we assume that the person who is able to sign a TX is the owner.

In all of this, your Ledger is a secure way to store your private key and a way to sign transactions. Your private key never leaves it, which makes it quite secure.

To conclude, when you "transfer your BTC to your Ledger" you in fact "send your BTC to the public address secured by the Ledger".