If I transfer a domain name from registrar 1 to registrar 2, would the authorization codes from these registrars be different? I read that auth codes are unique to each domain, but are they unique to each registrar too?
Yes, the authorization codes would be different. When transferring a domain you would need to obtain the authorization key from the current registrar. Then, after the transfer is complete the domain is in a sense re-registered with the new registrar and given a new authorization key for transfers.