Your coins are not actually stored in your hardware wallet and never actually leave the blockchain. What your hardware wallet stores is the private keys which allow you to "unlock" and spend your coins. The seed phrase is used to deterministically generate those private keys, so the same seed phrase will always generate the same wallet with the same private keys accessing the same coins. By entering your seed phrase in to a second hardware wallet, then that hardware wallet simply uses it to generate and store the same private keys as on your primary hardware wallet.
You can read both Ledger's and Trezor's passphrase information pages here:
https://support.ledger.com/hc/en-us/articles/115005214529-Advanced-passphrase-security
https://wiki.trezor.io/Passphrase
Thank you so much! Your information was very, very helpful!