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An exception is usually

1. The act of excepting or the condition of being excepted; exclusion.

2. One that is excepted, especially a case that does not conform to a rule or generalization.

3. An objection or a criticism: opinions that are open to exception.

4. Law A formal objection taken in the course of an action or a proceeding.

Whereas and error is:

1. An act, assertion, or belief that unintentionally deviates from what is correct, right, or true.

2. The condition of having incorrect or false knowledge.

3. The act or an instance of deviating from an accepted code of behavior.

4. A mistake.

5. Mathematics The difference between a computed or measured value and a true or theoretically correct value.

The phrase "the exception proves the rule" is usually misused because the "proves" is an archaic usage meaning "tests".

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