What is the difference between continuous audit and continuous monitoring ?

The main different is that continuos audit is responsibility of internal audit (Independent from management), and the continuos process is responsibility of management.

Internal audit is part of the continuous monitoring system

When we discuss about continuous auditing we refer to the continuous collection of audit material from the systems, processes, transactions and controls in order to examine compliance with established policies and procedures.

 

When we discuss about continuous monitoring, we refer to the automated mechanism that gathers information from the systems to ensure management that they are operating as designed and all relevant processes, transactions etc. are run correctly

Audit is to do with records and see where things went wrong while Monitoring is to keep guarding continuously.

continuous auditing is defined as any method used by auditors to perform audit-related activities( including control and risk assessments) on a more continuous (occurring without interruption) or continual (occurring at repeated intervals.) basis.
Continuous control monitoring is an automated feedback mechanism for management to ensure that the systems and controls have been operating as designed and transactions are processed appropriately.