How many times have you been speaking in English, and you make a silly mistake? For instance, "Yesterday, I go to work." You know you should have said, "went." You just made a mistake.
Mistakes are an accident. You know it's wrong, but the wrong word slips out.
An error, on the other hand, is something you don't know. It's grammar you haven't learned yet or vocabulary you haven't learned the nuance of yet. Errors are interesting because it gives you a chance to learn something for the first time.
Many people find mistakes boring. "Yesterday, I went to work, Yea, yea, yea. I got it." It's not fun to re-study basic points. But it is very important.
When you make a mistake, the listener doesn't know it's just a mistake. If you are speaking in a business situation, you'll lose a little of the listener's respect. If you make mistakes in speaking tests, you will get a very poor score.
If you ignore your mistakes, your English will not improve.
What should you do?
There are two steps: 1) now; and 2) later.
1. NOW: When your mistake is corrected, pay attention. Repeat the correction with variation, "Yesterday, I went... right, I went yesterday, went yesterday." Make a note to review later.
2. LATER: Review the note you made of the correction. You will forget most things quickly, so notes and review are vital.
So, what's the difference between an error and a mistake? For a speaking test assessor, nothing. They are the same. So, take both seriously.