Short answer
The short answer
A passkey is the stronger way to sign in where a service offers one, because it can’t be typed into a fake website or read out to a scammer. Authenticator codes still matter wherever passkeys aren’t available, and an account can have both.
New to the terms? Start with what two-factor authentication is. More guides: why a code in an app beats a code by text message, and what to do if you lose your phone.
What each is
What each one is
The FIDO Alliance says a passkey “is an authentication credential based on FIDO standards, that can be stored on your phone or computer”, and that you sign in “with the same process that they use to unlock their device”. Apple adds: “Passkeys sync across a user’s devices using iCloud Keychain.”
An authenticator code is a short number your app works out and shows for a short time. You type it in after your password.
Both
Using both
You don’t have to choose. Google says adding a passkey “doesn’t change or remove any authentication or recovery factors” already on your account, and “you still have the option to use your password to sign in to your account.”
So a sensible order is to add a passkey where you can, and keep your authenticator app and backup codes in place as the fallback until you are sure you can get back in.