Yes, your Recovery seed is unique but you don’t use it to directly access your wallet. It’s usually stored in a safe place until you really need it.
Your wallet is a listing of your funds in the blockchains, done by the Discovery procedure. You don’t need your Recovery seed at hand to access your wallet in everyday operations. When you connect your Trezor device, you only need your PIN (if used) to logon and a Passphrase (if you’re accessing a Hidden wallet). Inside your device is a generated Private key, derived from your Recovery seed, which is used to access your funds in the blockchains.
The Recovery seed is needed only if you need to restore your wallet because you’ve lost or damaged your Trezor device, thereby losing your key to access your funds in the blockchains. If you then acquire a new Trezor device, you can recreate the exact same keys again.