Error: A discrepancy between a computed, observed, or measured value or condition and the true, specified, or theoretically correct value or condition.

Failure: The inability of a system or component to perform its required functions within specified performance requirements.

Bug: A fault in a program, which causes the program to perform in an unintended or unanticipated manner.

Fault: An incorrect step, process, or data definition in a computer program, which causes the program to perform in an unintended or unanticipated manner.

Fault & Mistake: wrong coding done by Developers
 
Bug/Defect : A bug or defect is a flaw in a system or system component which may cause the system or the system component fail to  perform its desired action.