Difference between error and mistake

[Guest]

Test No. incompl/advan-53 "Invoices", question 6

Just as we were about to leave the restaurant, the waiter came running up to apologize there had been a ......... in the bill.

(a) error
(b) trip
(c) mistake
(d) damage

Test No. incompl/advan-53 "Invoices", answer 6

Just as we were about to leave the restaurant, the waiter came running up to apologize there had been a mistake in the bill.

Correct answer: (c) mistake

Your answer was: correct
_________________________

Well, by coincidence I took "mistake". However, I wonder where is the difference between "error" and "mistake".
Can you help me?

[Torsten]

Mistake an error could work both in this sentence but the word error requires 'an' as the indefinite article.

TOEIC listening, photographs: People shopping