What is the difference between Bug, Error and Failure?

Bug-A defect in the system that prevents it from behaving in the expected way e.g. a user is provided with User name and Password through which he can enter a Portal.

Now even after entering correct User name and Password User is not able to login into the system, such a situation arise due to a bug in the System.

Error-Error is a situation where system does not behave in the expected way due to an error committed by the user.

E.g. In the same example of logging to portal if system has a constraint that user name should always be entered in lower case and User enters the name in upper case then system would throw an error and would not allow user to login.

Failure-A situation where system deviates from expected behavior. In basic layman language system was build to match some requirement but the end product deviated from the set requirements.

E.g. For the same example to login to Portal, requirement says there should be a Forgot Password Link which would provide a feature to send a new password in case User forgets his password and by entering his User name he can receive new password. Now if the Login page has no such link then that is a failure as in case User forgets his password he cannot login to his portal.