Bitwarden Authenticator is a standalone app that is available for everyone, even non-Bitwarden customers.
In its current release, Bitwarden Authenticator generates time-based one-time passwords (TOTP) for users who want to add an extra layer of 2FA security to their logins.
There is a comprehensive roadmap planned with additional functionality.
Available for iOS and Android
Would it count if the application is the same but all the TOTP is handled by a different database with a different passphrase?
Depends on how they got broken