Audit is a function assigned to an office with staff responsible for its execution. In this definition of control, audit is one way to check controls. Authorize Official decision to confirm that a transaction may occur. To authorize is to give permission to take an action. The action is then forwarded for processing and approval.
Authorization is the precondition to approval, and is part of the initiation of a process.
One may authorize without approval, assuming they have the delegated authority. One may NOT approve without authorization. The P.I. is accountable for ensuring the transaction meets the business objectives and falls within the allowable budget. The Service Center is accountable for ensuring it is processed appropriately. This is a global view of control, inclusive of all actions, including, but not be limited to, developing policies and procedures, assigning responsibilities, assigning authorizations and accountabilities, monitoring and reporting activity, and establishing review or audit points within a process.