a bug is:
error; failure; defect; fault;
a bug is:
error; failure; defect; fault;
It depends on the type of the bug. Many programming languages will Log different types of bug. For your four terms, I would interpret them as follows:
Error: A general 'something's gone wrong'. I kind of catch-all term.
Failure: Something's gone wrong, and it's not the user's fault.
Defect: Something is fundamentally wrong, and is unlikely to be fixed.
Fault: Usually associated with Hardware (see: ServerFault)
Yes, it is all of those things. Or none of them.
Take any of those terms, and throw them into Thesaurus.com, and come up with any number of terms that you'd like. It doesn't really matter - all that matters is the context in which the bug is defined.
A "bug" could be a typo. Or, it could be a catastrophic error that, say, causes a returning spacecraft to careen into space.
To quote the Software Engineering Body of Knowledge
Typically, where the word “defect” is used, it refers to a “fault” as defined below. However, different cultures and standards may use somewhat different meanings for these terms, which have led to attempts to define them. Partial definitions taken from standard (IEEE610.12-90) are:
Error: “A difference…between a computed result and the correct result”
Fault: “An incorrect step, process, or data definition in a computer program”
Failure: “The [incorrect] result of a fault”
Mistake: “A human action that produces an incorrect result”
So depending on what you really mean by bug, it could mean any one of those things. Normally, I tend to think of a bug as either an error, or a fault caused by a mistake and manifested in a failure, according to those definitions.
I use term "bug" when I refer to a logical error, which is different to exception in my opinion.
Originally a bug was an actual insect. When computers were made up of vacuum tubes instead of silicon chips, bugs sometimes flew into them, got electricuted, and caused a tube to fail or a short circuit.
The term lived on in the computer genre, and came to mean any fault in a program itself.
Errors other than program bugs, is usually caused by incorrect input or hardware failures. However, usually most incorrect input and hardware failures should be handled gracefully by a program, so if a program crashes because of those it's a combination of external errors and bugs in the error handling.
Powell is the go-to references for this, Delta-4: A Generic Architecture for Dependable Distributed Computing
In fault-tolerant computing the path goes like so:
fault -> error -> failure -> fault -> ...
A fault is a latent problem or bad action, say cosmic ray or bug, software or hw design.
A fault causes an error, where the system doesn't do what it's expected to do.
This fault causes an error as the system does something it's not supposed to do.
In this taxonomy a bug is a fault, it turns into an error when the code path is executed and this causes a failure.