Both words mean a wrong action due to bad judgment or ignorance. They are often used interchangeably, while they have their proper way of usage. In formal or technical context, the use of error is appropriate, and in computing, too, error is the fitting term for any kind of mistake or fault. Mistake, on the other hand is often used in causal English. In language learning, mistake is natural, which the language learner commits while learning, but if they are corrected, they should not come up anymore. If particular mistakes occur more often and they are not corrected by the learner, they are called errors. To sum up, error is considered to be more severe than mistake, and error is more suitable for formal context, while mistake is rather used in casual conversation.
