The password itself is not stored in AD in decryptable form. As I understand it what is stored is a hash of the password and the date/time when the password was set. When a user logging on enters the password that value and the date/time when the password was last set are used to re-calculate the stored hash. if this is the same as the stored hash, the assumption is that the user entered a valid password.
Full Definition of CREDENTIAL. 1. : something that gives a title to credit or confidence; also: qualification 3a. 2. plural: testimonials or certified documents showing that a person is entitled to credit or has a right to exercise official power.
Authentication is the process that allows an application to verify that a person (or another application, smart card, and so on) is the one that it claimed to be when connecting with it. Authorization defines a user's rights and permissions in a system. After a user is authenticated, authorization determines what that user has the authority to do on the system. Authorization, therefore, is typically assumed to follow authentication.