Product key

If you lost your Recovery Key

As long as you remember your Apple ID password and still have access to one of your trusted devices, you can sign in and create a new Recovery Key.

1. Go to your Apple ID account page.
2. Sign in with your password and trusted device.
3. In the Security section, click Edit > Replace Lost Key.

Keep your new Recovery Key in a safe place. Your old Recovery Key won't work anymore and you can't use it to reset your password or access your account.

If you can't sign in with two-step verification using your Apple ID ...

My knowledge says you can have both. Please see the pic below

The pros and cons of the two are... Please see the table below