A fault is synonymous to mistake and error, although these words differ in context depending upon how they are being applied. A fault may be caused by misjudgment, negligence, and forgetfulness. When one is at fault, it may be because someone is ignorant, not paying attention, or is judging things poorly. It is considered to be a weakness, or a shortcoming, or even a mistake.
A fault may also refer to a physical or intellectual inadequacy. Quite often, it demonstrates a person's responsibility for a bad situation or event. On the other hand, failure is the condition or state of not being able to meet an envisioned objective. It is the opposite of success and is dependent on how it is used. There are also good failures and bad failures. Good failures involve growth, change, and learning from mistakes.