Mistake vs Error

There is some overlap in these terms, which both refer to a "wrong" action -- for example, a problem gotten wrong on an exam could be called an error or a mistake -- but there are also significant differences in usage and connotation.

A mistake, generally speaking, is a choice that turns out to be wrong.  It could be something you decide to do on your own initiative that you later regret:

- "You're making a mistake -- you'll regret this!"
- "Coming here was a mistake -- this trip has been a waste of my time."
- "Don't feel bad, everyone makes mistakes."

... or a misidentification or miscalculation where a wrong answer is produced:

- "I thought it was her, but I was mistaken."
- "That can't be his fingerprints, the computer must have made a mistake!"
- "I made a mistake on problem 3."

A mistake is wrong because the outcome is found to be wrong.  Mistakes are made when a free choice is made, and later called "mistakes" when they score badly in the context of the goal of determining a particular answer, or else they simply turn out to be bad choices in some later assessment.

Errors, on the other hand, are made with reference to some ideal code, model, or set of rules that would have dictated a different action.  The action was wrong because it was different from the "right" or normal one under the circumstances.

Error is a more formal word and has various technical meanings:

- In sports, particular rules violations are "errors."  A "mistake" would be the coach or the referee making a poor strategic decision or a wrong call.

- Computers produce "errors" when they aren't able to perform some step as programmed, such as connecting to the Internet or saving a file.  Computers make mistakes only by spitting out the wrong answer to a question.  (We don't consider computers to originate actions willfully and be held accountable for them, except in humorous personification, so we would only jokingly say, "The computer made a big mistake by not saving my file."  However, we could completely seriously say, "The airport computer made a mistake in calling me Davidmr Greenspan," because it is stating a wrong fact.)

- In science, "experimental error" is the completely normal and expected deviation of the measurements from the theory.  Measurements are never perfect; they always contain "error" due to imperfect conditions, instruments, and models, and the question is only whether the error matches expectations in its size and nature.  A "mistake," on the other hand, could be any wrong step by the experimenters, particularly a wrong choice in experimental set-up, or else a miscalculation or misidentification, especially if it leads to a wrong conclusion.

To confuse matters a little, any mistake that occurs in the context of a formal process held to a clear standard can be called an error in something: an error in judgment, a calculation error, an error in experimental set-up.  We assume for the sake of the phrase that calculation and even experimental set-ups are tightly governed by known procedures.

An "error in judgment" is typically a moral or ethical lapse, precisely because it implies there is some code governing the judgment in question.  Similarly, "to err" in the oldest and grandest sense is literally to stray from the righteous path.