A bug is an error, mistake, failure in a computer program 
that prevents it from working as intended. Bugs arise from 
mistakes and errors made by people, in either a program's 
source code or its design.

A defect is one that causes a reproducible malfunction. A 
malfunction is considered reproducible if it occurs 
consistently under the same circumstances.

Bug :  Any missing functanility on any action that 
performed by the system which is not supposed to do:
"Is an error found before the application goes to 
production"
*wrong functanility  *Extra or Unwanted Functanilty.
* Missing functanility .

Defect: A defect is the varience from the desired attribute 
of a system or application.
"Is an error found after the application goes into 
production"
* Defect from product specification.
* variance from user expectation.

Bug & defect is same.many people think that these are two 
different things.If you still have any doubt abt it You can 
refer ISTQB syllabi for it.These are just two terms used 
for same thing.It is also called as Incident or Fault.

Bug/Defect : It is flaw in component or system which can 
cause component or system to fail to perform its required 
operation.

You should also know defination of error & failure to 
understand these terms clearl.

Error : Incorrect human action.

Failure : Departure from expected behaviour.

User made mistakes while using software that result in 
error.then because of this error system fails to perform 
its intended operation so it leads to defect/Bug .If these 
Bug occured during execution system can fail so bug leads 
to failure of system.

Error-> Bug - > Failure.