What is the Difference between Error, Fault Failure and Bug ?

Error: It refers to the discrepancy between computed or measured value and theoretically correct value. i.e. Difference between actual output and correct output of the software.

Fault:  Fault is the basic reason for software malfunction. i.e. Fault is a condition that causes a system to fail in performing its required function.

Failure: Is the inability of the system or component to perform a required function according to its specifications.  A Software failure occurs if the behavior of the software is different from the specified behavior.

Bug:  Non Functionality to a functionality

Presence of an error implies that a failure must have occurred, and the observance of a failure implies that a fault must be present in the system.

During the testing process only failures are observed by which presence of fault is deduced.  The actual faults are identified by separate activities commonly referred to us 'debugging'.

In other words, for identifying faults after testing has revealed the presence of faults the expensive task of debugging has to be performed.    This is the reason 'why testing is expensive.'