"Hardware Wallets" are not Bitcoin wallets, they are signing devices. A device to store and manage private keys securely. Bitcoin wallets have chain state (access to the blockchain/ledger) and are capable of creating transactions. With the term "Signing Device" or "Bitcoin Signer" we hope to disambiguate.

This is a better term because it frames the process in terms of speech/action. "This is my signature", "using my signing device". It also help show how non-signing wallets (ie "hosted" or "web" wallets) take away your capacity to trully own, sign.